Suppose that a cyclist began a 364 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after 6.5 hr and the car traveled 31.4 mph faster than the bicycle, find the average rate of each. The car's average rate is _ mph. The bicycle's average rate is _ mph. (Type an integer or a decimal.)

Question

Mathematics

Sarai Mcneil

Yesterday, 22:44

Suppose that a cyclist began a 364 mi ride across a state at the western edge of the state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after 6.5 hr and the car traveled 31.4 mph faster than the bicycle, find the average rate of each. The car's average rate is _ mph. The bicycle's average rate is _ mph. (Type an integer or a decimal.)

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Hays · Answer 1

The car's average rate is 43.7 mph. The bicycle's average rate is 12.3 mph.

To get this solution, let the bicycle's average rate be (x) and the car's average rate be (x + 31.4) mph.

Distance = Speed x Time

364 = (x + x + 31.4) 6.5

364 = (2x + 31.4) 6.5

364/6.5 = 2x + 31.4

56 = 2x + 31.4

56 - 31.4 = 2x

24.6 = 2x

24.6/2 = x

12.3 = x

x = 12.3 mph

x+31.4 = 43.7 mph