Question

Two cyclist start at the same point and travel opposite directions. One cyclist travels 8 mi/h slower than the other. If the two cyclist are 144 miles apart after 4 hours , what is the rate for each cyclist? Please answer ASAP

Answer 1

slower cyclist = 14 mph

faster cyclist = 22 mph

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Work Shown:

x = rate of slower cyclist

x+8 = rate of faster cyclist, since this person travels 8 mph faster

After 4 hours, the slower cyclist covers 4x miles while the faster cyclist covers 4(x+8) = 4x+32 miles. In total, they cover 4x+4x+32 = 8x+32 miles. In other words, this is the distance between them after 4 hours.

Set this equal to 144 and solve

8x+32 = 144

8x = 144-32

8x = 112

x = 112/8

x = 14 is the slower cyclist's speed in mph

x+8 = 14+8 = 22 is the faster cyclist's speed in mph

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as a check:

distance = rate*time = 4*14 = 56 miles is covered by the slower cyclist

d = r*t = 4*22 = 88 miles is covered by the faster cyclist

56+88 = 144 miles is the total distance between the two cyclists after 4 hrs

the answers are confirmed