ALGEBRA READINESS

LESSON 6-4Warm Up Lesson 6-4 Warm-Up

ALGEBRA READINESS

LESSON 6-4Warm Up Lesson 6-4 Warm-Up

ALGEBRA READINESS

“Application of Rates” (6-5)

How do you find the total distance if you are given time traveled at two or more speeds?” work?

By dimensional analysis, the product of time and speed (rate) is total distance traveled, or d = rt.

Proof: hours • = • = = miles

Sometimes, you have to two or more times and rates in a problem. In these cases, you will need to find the distances at each rate and add them together.

Example: It takes you 1.25 hours at 7 mi./hr. to bike from your house to the lake. Then, it takes you 1 hour to bike to the store at 9 mi./hr. What is the total distance traveled from your home to the store?

Find the distance for each part of the trip.

mileshour

miles1

You bike a total of 17.75 mi.

ALGEBRA READINESS

A bus is driven from the center of a city to its first stop.

The trip takes 0.25 h at 15 mi/h. The bus then continues on the

highway to a park-and-ride station. The trip takes 0.50 h at a

speed of 56 mi/h. What is the total distance traveled by the bus?distance to stop = rate to stop • time to stop

mi h

= 15 • 0.25 h

= 3.75 midistance to station = rate to station • time to station

mi h

= 15 • 0.50 h

= 28 mi

The bus travels a total of 31.75 miles.

total distance = 3.75 mi + 28 mi Add the two distances.

= 31.75 mi Simplify.

Applications of RatesLESSON 6-4

Additional Examples

ALGEBRA READINESS

How do you find the average speed?s” work?

Since d = rt, where d = distance , r = rate (speed), and t = time:

average rate (speed) = distance / time

Proof: If we divide both sides of d = rt by t to isolate r:

= r or r = (Example: )

Example: A car travels 35 mi./hr. for 1 hour. It then travels 50 mi./hr. for 1.5 hours. What is the cars average speed over the total distance?

d t

d t

miles hours

“Application of Rates” (6-5)

ALGEBRA READINESS

A speed skater travels 8 m/s for 30 s, and then travels 6

m/s for 18 s. What is the skater’s average speed over the total

distance?mstotal distance = 8 • 30 s + 6 • 18 s = 348 mm

s

total time = 30 s + 18 s = 48 s

average speed = total distancetotal time

Average speed is the total distance divided by the total time.

= 348 m48 s

Substitute the values for total time and total distance.

= 7.25 ms Simplify.

The skater’s average speed is 7.25 m/s.

Applications of RatesLESSON 6-4

Additional Examples

ALGEBRA READINESS

At a poster store, the shipping cost of a poster varies directly

with its width. It costs $12 to ship a poster that has a width of 16 inches.

What is the shipping cost of a poster that has a width of 20 inches?

$1216 in.

= 0.75 • $in.

Find the unit rate.

20 • 0.75 = 15 Multiply the width by the unit rate.

A 20-inch poster will cost $15 to ship.

Check for Reasonableness Use dimensional analysis to check the units: in. • = $. The question asked for cost, so the answer is reasonable.

$in

Applications of RatesLESSON 6-4

Additional Examples

ALGEBRA READINESS

Find each total distance.

55 mi/h for 1.5 hours and 60 mi/h for 0.75 hours

2. 8 meters per second for 2.5 seconds and 6 meters per second for 1.8 seconds

The quantities vary directly. Find each missing quantity.

3. 53 miles : 2 gallons; ? miles : 5 gallons

4. 16 feet : 2.5 seconds; ? feet : 5.6 seconds

1. 127.5 miles

30.8 meters

132.5

35.84

Applications of RatesLESSON 6-4

Lesson Quiz