Time Rates

25 Two cars that may collide at 12:30 PM

Problem 25
One city E, is 20 miles north and 20 miles east of another city, F. At noon a car starts south from E at 40 mi/hr, at 12:10 PM, another car starts east from F at 60 mi/hr. Find the rate at which the cars approach each other between 12:10 PM and 12:30 PM. What happens at 12:30 PM?

22-24 One car from a city starts north, another car from nearby city starts east

Problem 22
One city C, is 30 miles north and 35 miles east from another city, D. At noon, a car starts north from C at 40 miles per hour, at 12:10 PM, another car starts east from D at 60 miles per hour. Find when the cars will be nearest together.

19-21 Two cars driving in parallel roads

Problem 19
One city A, is 30 mi north and 55 mi east of another city, B. At noon, a car starts west from A at 40 mi/hr, at 12:10 PM, another car starts east from B at 60 mi/hr. Find, in two ways, when the cars will be nearest together.

17-18 Rate of shadow in the wall of a building

Problem 17
A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building.

15-16 Movement of shadow from light at eye level

Problem 15
A light at eye level stands 20 ft from a house and 15 ft from the path leading from the house to the street. A man walks along the path at 6 ft per sec. How fast does his shadow move along the wall when he is 5 ft from the house?

13-14 Water flowing into trapezoidal trough

Problem 13
A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If water flows in at 10 ft3/min, find how fast the surface is rising, when the water is 6 in deep.

11-12 Two trains; one going to east, and the other is heading north

Problem 11
A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM.

10 - A boy on a bike

Problem 10
10-figure-47-boy-on-a-bike.jpgA boy on a bike rides north 5 mi, then turns east (Fig. 47). If he rides 10 mi/hr, at what rate does his distance to the starting point S changing 2 hour after he left that point?

08-09 Rate of movement of shadow on the ground

Problem 08
A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast does the end of his shadow move?

06-07 Ladder slides down the wall

Problem 06
A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.


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