<PRE><B>Question 282321</B>
A jogger started a course at 4.5 mph.  A cyclist started the same course 1 hour later at an average speed of 14 mph.  How long after the jogger started did the cyclist take over the jogger?  Round to the nearest tenth of an hour.

let the cyclist meet the jogger at a distance x from the start

He starts after 1 hour after the jogger starts

so jogger would have traveled 4.5 miles by that time.

distance traveled by jogger when cyclist meets him will be x-4.5 miles

the time they travel after cyclist starts is the same.

time taken by jogger = x-4.5 / 4.5 

time taken by cyclist = x/14


x/14 = x-4.5 /4.5

4.5x/14 = x-4.5

4.5x = 14(x-4.5)

4.5x= 14x- 63

-9.5x=-63

x= -63/-9.5

x=6.6 miles the distance they meet from the start

Time taken by jogger to jog (6.6-4.5) = 2.1 miles =  2.1/4.5= 0.46 hours

the cyclist meets the jogger after 1.46 hours after the jogger started





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