suppose that a cyclist began a 442 mi ride across a state at

suppose that a cyclist began a 442 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 meet after 6.5 hr and the car traveled 31.2 mph faster than the icycle, find the average rate of each

Solution

Let the speed of the cyclist be x. Then the sppeed of the car is x + 31.2. The distances travelled by the cyclist and the car in 6.5 hours are 6.5x and (6.5)( x + 31.2) respectively. Since the cyclist and the car meet in 6.5 hours after having started simultaneously from the western and the eastern edges of the state respectively and since the distance between the western and the eastern edges is 442 miles, the cyclist and the car together have travelled a distance of 442 milles in 6.5 hours. Therefore 6.5x + ( 6.5) (x + 31.2) = 442 or, x + x + 31.2 = 442/6.5 or, 2x + 31.2 = 68 Therefore 2x = 68 - 31.2 = 36.8 so that x = 1/2 (36.8) = 18.4 miles per hour. Thus the average speed of the cyclist is 18.4 mph. Therefore, the average speed of the car is 18.4 + 31.2 = 49.6 mph.