Time – rate Problems1. A balloon is rising vertically over a point A on the ground at the rate 15 ft/sec. A point B on the ground is level with and 30 ft. from A. When the balloon is 40 ft. from A, at what rate is its distance from B changing?2. Ship A is 15 miles east of O and moving west at 20 mi/hr; ship B is 60 miles of south of O and moving north at 15 mi/hr.a) Are they approaching or separating after 1 hr and at what rate?b) Are they approaching or separating after 3 hrs and at what rate?c) When are they nearest together?3. Sand is being dropped at the rate 10 m3/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?4. A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light at the rate of 5 ft/sec, how fast is his shadow lengthening and at what rate is the tip of the man’s shadow moving?5. A man 6 ft tall is walking toward a building at the rate of 5 ft/sec. If there is a light on the ground 50 ft from the building, how fast is the man’s shadow on the building growing shorter when he is 30 ft from the building?6. A ladder 7 m long is leaning against the wall. If the bottom of the ladder is pushed horizontally toward the wall at 1.5 m/sec, how fast is the top of the ladder sliding up the wall when the bottom is 2 m from the wall?7. A horizontal trough is 16 m long , and its end are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m. Water is being poured into the trough at the rate of 10 m3/m. How fast is the water level rising when the water is 2 m deep?8. Water is poured at the rate of 8 ft3/min into a conical-shaped tank, 20 ft deep and 10 ft in diameter at the top. If the tank has a leak in the bottom and the water level is rising at the rate of 1 in/min, when the water is 16 ft, how fast is the water leaking?

9. The supply equation for a certain commodity is x =1000 , where x units are supplied per month

when p dollars is the price per unit. Find the rate of change in the supply if the current price is $20 per unit and the price is increasing at the rate of $0.50 per month.10. This week a factory is producing 50 units of a particular commodity, and the amount being produced is increasing at the rate of 2 units per week. If C(x) dollars is the total cost of producing x units and

C(x) = , find the current rate at which the production cost is increasing.

Time – rate Problems1. A balloon is rising vertically over a point A on the ground at the rate 15 ft/sec. A point B on the ground is level with and 30 ft. from A. When the balloon is 40 ft. from A, at what rate is its distance from B changing?2. Ship A is 15 miles east of O and moving west at 20 mi/hr; ship B is 60 miles of south of O and moving north at 15 mi/hr.a) Are they approaching or separating after 1 hr and at what rate?b) Are they approaching or separating after 3 hrs and at what rate?c) When are they nearest together?3. Sand is being dropped at the rate 10 m3/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?4. A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light at the rate of 5 ft/sec, how fast is his shadow lengthening and at what rate is the tip of the man’s shadow moving?5. A man 6 ft tall is walking toward a building at the rate of 5 ft/sec. If there is a light on the ground 50 ft from the building, how fast is the man’s shadow on the building growing shorter when he is 30 ft from the building?6. A ladder 7 m long is leaning against the wall. If the bottom of the ladder is pushed horizontally toward the wall at 1.5 m/sec, how fast is the top of the ladder sliding up the wall when the bottom is 2 m from the wall?7. A horizontal trough is 16 m long , and its end are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m. Water is being poured into the trough at the rate of 10 m3/m. How fast is the water level rising when the water is 2 m deep?8. Water is poured at the rate of 8 ft3/min into a conical-shaped tank, 20 ft deep and 10 ft in diameter at the top. If the tank has a leak in the bottom and the water level is rising at the rate of 1 in/min, when the water is 16 ft, how fast is the water leaking?

9. The supply equation for a certain commodity is x =1000 , where x units are supplied per month

when p dollars is the price per unit. Find the rate of change in the supply if the current price is $20 per unit and the price is increasing at the rate of $0.50 per month.10. This week a factory is producing 50 units of a particular commodity, and the amount being produced is increasing at the rate of 2 units per week. If C(x) dollars is the total cost of producing x units and

C(x) = , find the current rate at which the production cost is increasing.