need answer to a written word problem

Question

Two cyclists leave a city at the same time, one going east and the other going west. The west bound cyclist bikes at 3mph faster than the east bound cyclist. After 2 hours they are 42 miles apart. How fast is each cyclist riding?

Answer 1

distance = rate*time

In this case 42 will be the sum of the distances travelled by each cyclist.

One cyclist has a rate of r, the other will be r+3.

The time for both is 2 hours

 

42 = 2r + 2(r+3)

42 = 2r + 2r + 6

42 = 4r + 6

36 = 4r

9 = r

 

The slower cyclist is going 9 mph

The other is going r+3 = 12 mph

 

Check:  9(2) = 18

           12(2) = 24

           18 + 24 = 42   Answer checks