TIME SPEED & DISTANCETIME & WORK, PIPES & CISTERNS

TIME SPEED & DISTANCEThere is only one formula relating the three parameters Distance (D), Speed (S) and Time (T) and it is D = S xT

CONCEPT 1: Average Speed : Average speed is always the total distance travelled / the total time taken. Average speed = If a certain distance D is covered at S1 km/hr and on return covered at S2 km/hr then, the average speed is not (S1 + S2) / 2 but is calculated as below:

Total distance = D + D = 2D and Total time = + Av speed = =

Eg : K travels from A to B at a speed of 3 kmph for of the distance and 4 kmph for the remaining distance, what is his average speed from A to B.Total dist = DTotal time = + = = Av. Speed = = = 3.2 kmph

CONCEPT 2: Relative Speed ( SR ) When two objects are travelling at speeds of S1 & S2, the SR between them :a. When they are travelling in opposite directions is S1 + S2 andb. when they are travelling in the same direction is S1 S2.SR is used by in calculations by bringing one object to a standstill and allowing the other object travel at the speed = SR.

Eg 1: Two trains start at the same time from A and B and proceed towards each other at speeds of 15 and 35 kmph respectively. If the distance between A & B is 400 kms at what time and distance will they cross each other?By bringing A to a standstill and allowing B to travel at RS we know the distance travelled by the second train to meet the first train is 400 kms. Therefore D / SR will give the time taken for the two trains to meet i.e. 400/(15+35) = 8 hours. DA = Speed X time = 15 x 8 = 120 kms and DB = 35 x 8 = 280 kms. Ans : The trains will meet after 8 hours of starting and will meet 120 kms from A or 280 kms from B.

Eg 2 : Two trains start at the same time from A and B. Train A travels towards B and train B travels away from A. Speeds of train A and train B are 35 and 15 km/hr respectively. If the distance between A & B is 400 kms at what time and distance will Train A meet Train B?By bringing train B to a standstill and allowing the train A to travel at RS we know the distance travelled by train A to meet the train B is 400 kms.

Therefore Dist / RS will give the time for the two trains to meet i.e. 400/(35-15) = 20 hours. Distance travelled by train A = Speed X time = 35 x 20 = 700 and the distance traveled by train B = 15 x 20 = 300.

The trains will meet after 20 hours of starting and will meet 700 kms from A or 300 kms from B.

CONCEPT 3: Calculating the length of the train based on the time taken by the train to pass a fixed pointEg 3: A train of length 200 meters passes a pole in 10 secs. The speed of the train is 200/10 = 20 m/s.

CONCEPT 4: Calculating the length of the train based on the time taken by the train to pass a fixed object with a length of its ownEg 4: If a train of length 200 meters crosses a 300 m platform in 20 secs.The speed of the train is (200+300)/20 = 25 m/s.

CONCEPT 5: When the medium in which the articles are moving has a velocity of its own.If the speed of a boat in still water is Sb & speed of the current/ stream is Sc, then

Speed of boat while going downstream = Sb + Sc andSpeed of boat while going upstream = Sb - Sc

ABCONCEPT 6 : Circular Races:

Eg: If A and B race around a circular track of length 300 meters at a speed of 5 m/min and 9m/min respectively i. Where and when will B overtake A andii. When will A & B meet at the starting point againThe SR of A & B = 9-5 = 4 m/min and the distance D = 300 m. Therefore time taken for A & B to meet will be = D/RS = 300/4 = 75 min. In 75 min A would have travelled 75 x 5 = 375 ms and B would have travelled 75 x 9 = 675 ms. i. A would have completed 1 round and be at a point 75 ms from the start and B would have completed 2 rounds and be at the same point. Hence B will overtake A after 75 min and at a point 75 ms from the start.ii. A will come to the starting point every 300/5 mins and B will arrive at the starting point every 300/9 mins. The time they will meet at the starting point again will be the LCM of the two times ie LCM (300/5, 300/9) = 300/1 = 300 mins

PIPES & CISTERNS

All the concepts applicable to Time & Work apply to Pipes & CisternsHowever there is one fundamental difference.In Time & Work there cannot be negative work, but in Pipes & Cisterns the pipe can be a drain instead of inletSowhen pipe A takes A hrs and Pipe B takes B hours to fill a tank and pipe C takes C hours to empty a tank and each of them are opened for a hrs, b hrs and c hrs respectively then the equation becomesa/A + b/B - c/C = 1

Time and Work

Work problems can be split into 2 categories:

CONCEPT 7: Where everyone works with the same efficiencyEg: 30 men take 15 days working 8 hours a day to complete the job. How many men, working for 20 days at 4 hours day will be needed to complete the same job?The Quantum of work done = No.of men x No.of days x No.of hours/dayHere the quantum of work done W by both groups is the same.We, therefore, can equate as belowM1D1H1 = W = M2D2H230 x 15 x 8 = M2 x 20 x 4M2 = 45 men

CONCEPT 8: Where everyone works with different efficiency.Eg: A can do a piece of work in 8 days by himself and B can complete the same work in 10 days by himself. If works for 4 days and then stops, how long will B take to complete the rest of the work?

If A can complete the work in 8 days by himself, he can complete 1/8 of the work in 1 day, so if A works for 4 days he can finish 4/8 ( i.e. or 50% ) of the total work.

Now B has to complete the remaining of the work. He takes 10 days to complete the full work hence in 1 day he can do 1/10 of the work. Therefore to complete or 50% of the work B will have to work for 5 days

To generalize, If A can do a job in A days by himself and B can do the same job in B days by himself and if C can do the same job inC days by himself AND if they work for a days, b days and c days respectively to complete the job , then + = 1 (This 1 is known as UNIT WORK or 100% of the work)

Our problem can be worked using this formula as under = 1. b = 5

CONCEPT 9: People working with different efficiency, work together to finish a piece of workNow, if they both work together for x days to finish the job. The number of days to finish the job can be found by changing the formula as below = 1 ; Eg: A can do a piece of work in 8 days by himself and B can complete the same work in 12 days by himself. If works for 4 days and then stops, how long will B take to complete the rest of the work? = 1 x = daysx = 4.8 days

CONCEPT 10: When theres a proportional variation between the effeciencies of the individuals Now, if they both work together for x days to finish the job and A is twice as efficient as B then the formula becomesx/A + x/2A = 1

CONCEPT 11: If A & B working together take x days to complete a job and A takes a days more when working alone and B takes b days more when working alone than when working together, find x Let the number of days A & B working together take be x, then the equation becomes + = 1Simplifying x = (ab)

1. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time will B take to do it? a. 45 days b.40 days c.35 daysd.30 days 2. A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. In how many days will the work be completed? a. 15 2/3 days b.14 1/3 days c.16 1/3 daysd.18 2/3 days 3. A alone takes 15 hours to produce 60,000 pieces which A & B can produce together in 10 hours. How many pieces will B produce in 15 hours? a. 20,000 b.25,000 c.30,000d.60,0004. A takes 12 hours more to complete a job than when he works with B and B takes 3 hours more to complete the same job when he works with A. How long will they take to complete the job together?a. 7.5 hrs b.6 hrs c.5 hrsd.4.5 hrs5. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? a. 24 hrsb.25 hrsc.20 hrsd.30 hrs6. A pipe can fill a tank in 15 hrs. Due to a leak in the bottom, it is filled in 20 hrs. If the tank is full, how much time will the leak take to empty the tank? a. 65 hrsb.60 hrsc.55 hrsd.50 hrs7. A tank is erected with two outlet pipes and one inlet pipe. The outlet pipe A is twice the size of outlet pipe B and inlet pipe C is twice the dia of B. If the tank gets full every 30 days when all three pipes are open, how long will it take inlet pipe C to fill the tank? a. 5 days b.7.5 days c.10 daysd.15 days 8. A pipe M can fill a tank in x hours jointly with another pipe N. By itself M takes (x + 8) hours to fill the tank. Pipe N takes (x+18) hours to fill the tank. Find the no.of days taken by M and N to fill the tank individually.a. 18, 28 daysb.20, 30 days c.22, 32 daysd. None of these

7. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time will B take to do it? a. 45 days b.40 days c.35 daysd.30 days 8. A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. In how many days will the work be completed? a. 15 2/3 days b.14 1/3 days c.16 1/3 days d.18 2/3 days 9. A alone takes 15 hours to produce 60,000 pieces which A & B can produce together in 10 hours. How many pieces will B produce in 15 hours? a. 20,000 b.25,000 c.30,000d.60,00010. A takes 12 hours more to complete a job than when he works with B and B takes 3 hours more to complete the same job when he works with A. How long will they take to complete the job together?a. 7.5 hrs b.6 hrs c.5 hrsd.4.5 hrs11. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? a. 24 hrsb.25 hrsc.20 hrsd.30 hrs12. A pipe can fill a tank in 15 hrs. Due to a leak in the bottom, it is filled in 20 hrs. If the tank is full, how much time will the leak take to empty the tank? a. 65 hrsb.60 hrsc.55 hrsd.50 hrs13. A tank is erected with two outlet pipes and one inlet pipe. The outlet pipe A is twice the size of outlet pipe B and inlet pipe C is twice the dia of B. If the tank gets full every 30 days when all three pipes are open, how long will it take inlet pipe C to fill the tank? a. 5 days b.7.5 days c.10 daysd.15 days 14. A pipe M can fill a tank in x hours jointly with another pipe N. By itself M takes (x + 8) hours to fill the tank. Pipe N takes (x+18) hours to fill the tank. Find the no.of days taken by M and N to fill the tank individually.a. 18, 28 days b.20, 30 days c.22, 32 days d.None of these

PROBLEMS

9. A certain numbers of men could do a piece of work in 60 days. If there were 8 more men, it could be finished in 10 days less. The number of men, in the beginning were: a. 45b.40c.35d.3010. Shree can do a work in 3 days. Sampath can do the same work in 2 days. Both of them finish the work together and get Rs .150. What is the Shrees share? a. Rs.60b.Rs.90c.Rs.100d.Rs.7511. The wages of 10 workers for six days in a week is Rs.1200. What is the one day wages for 4 workers? `a. Rs.480 b.Rs.120 c.Rs.100d.Rs.80 12. If a typist can type 75 pages of manuscript having 44 lines on each page and 16 words to the line in 5 days. How many pages of 30 lines each and 16 words to each line can she type in 6 days? a. Rs.143 b.Rs.132 c.Rs.110d.Rs.15413. A can do a piece of work alone in 12 days, while B alone can do it in 15 days, with the help of C they can finish it in 5 days. If they are paid Rs.960 for the whole work, what is the share of A? a. Rs.480 b.Rs.240c.Rs.320d.Rs.40014. In a factory assembly line, 20 workers can complete one third of a work in 20 days. How many more workers should be deployed to finish the rest of the work in 25 more days? a. 32 b.25 c.7d.5 1. I row from A to B against the current in 8 hrs. and from B to A in 2 hrs. If the speed of the river is 9 m/s, what is the speed, in m/s, of the boat in still water?a. 15b. 20c. 16d.22 2. A man rows 27 km downstream and 15 km upstream taking 4 hrs each time. Find his speed in km/hr in still water and the speed in km/hr at which the stream flows. a. 5.25 & 1.5b. 6 & 2.25c. 5.25 & 1.25d.7 & 193. A train traveling at 25 km/hr, leaves Delhi at 9a.m. and another leaves Delhi at 35 km/hr at 2p.m. in the same direction. How many kms from Delhi do they meet? a. 437.5 kmb. 450 kmc. 550 kmd.125 km4. Two trains 121 meters long and 99 meters long are running in opposite directions, the first at 40 km/hr and the second at 32 km/hr. In what time will they completely clear each other from the moment they meet? a. 11 secb. 10 secc. 22 secd.20 sec5. How long does a train 110 meters long running at 36 km/hr take to cross a bridge 132 meters in length? a. 24.2 secb. 25 secc. 25.4 secd.30 sec6. A car driven in fog passed a man walking at 3 km/hr in the same direction. He could see the car for 4 min and up to a distance 100m. What was the speed of the car? a. 4.5 kmphb. 5 kmphc. 6.3 kmphd.5.5 kmph7. In a 200 meter race A beats B by 60 meters and C beats B by 25 meters. In the same race who will win between A & B and what will be the difference in lengths run when the leader finishesa. A, 35 mb. A, 40 mc. C, 35 md. C, 40 m 8. Kumars driver leaves home for the office every day to pick up Kumar at the office exactly at 7:00 pm and return home. One day Kumar finishes an hour early and decides to walk home part of the way. He is picked up by his chauffer in between and reaches home 30 minutes earlier than normal. How many minutes has Kumar walked. a. 15 minb. 30 minc. 45 mind. 40 min PROBLEMS9. A man covers the distance between his house and office travelling at an average speed of 30 km/hr, he is late by 10 min. But, at a speed of 40 km/hr, he reaches his office 5 min earlier. The distance from his house to office is? a. 30 kmb. 35 kmc. 40 kmd.42 km10. Two trains start at the same time from Hyderabad and Delhi and proceed toward each other at the rate of 80 km and 95 km per hour respectively. When they meet, it is found that one train has traveled 180 km more than the other. Find the distance between Delhi and Hyderabad. a. 2100 kmb. 2200 kmc. 24400 kmd.2500 km11. Walking at 3/4th of his usual speed, a man is 1 hrs late. Find his usual travel time. a. 4.5 hrsb. 5 hrsc. 6 hrsd.5.5hrs12. If a boy goes to school at 6 km/hr and returns home at 4 km/hr, find his average speed.a. 6kmphb. 5.2 kmphc. 5 kmphd.4.8kmph13. I shall be 40 min late to reach my office if I walk from my house at 3 km/hr. I shall be 30 min early if I walk at 4 km/hr. find the distance between my house and the office. a. 14 kmb. 20 kmc. 22 kmd.25 km14. A man travels 120 km by ship, 450 km by rail and 60 km by horse taking all together 13 hrs 30 min. the speed of the train is 3 times that of the horse and 1 times that of the ship. Find the speed of the train, in km/hr? a. 60b. 66c. 40d.8015. A and B walk from P to Q, a distance of 21 km at 3 and 4 km/hr. B reaches Q, and immediately returns and meets A at R. Find the distance from P to R.a. 18 kmb. 22 kmc. 20 kmd.26 km16. A man travelling from A to B at 3 mph, takes half an hr rest at B, and returns to A at 5 mph. Total time taken is 3 hrs 26 min. Find the distance from A to B. (m = miles). a. 5.5 milesb. 6 milesc. 6.2 milesd.7 miles17. Walking 8/7th of this original rate, a man reaches his office 3 min early. Find the usual time he takes to reach office. a. 24 minb. 30 minc. 44 mind.50 min18. The ratio between the speeds of Meena and Teena is 2:3. Meena takes 20 min more than Teena to walk from A to B. If Meena had walked at double her speed, find the time she would take to walk from A to B. a. 40 minb. 50 minc. 30 mind.80 min