Jen rode her bike to visit her friend Who live 12 miles away on her way there her average paid with 7 mph faster than her way home if Jen spent a total of one h

Question

Jim recently rode her bicycle to visit her friends who live 12 miles away on her way there her average speed was 7 mph faster than on her way home if Jen spent a total of one hour bicycling find the two rates

Answer 1

 

 

Nevertheless, we can figure out how to solve this problem.

Outbound trip: D = (rate)(time)    12 = (x+7)(1-t)

Inbound trip:                            12 = (x)(t)   

Note that the rates differ by 7, with outbound being 7 mph faster, and total times = 1.

 

In the first equation, after distributing, you get 12 = x - tx + 7 - 7t

From the second equation we can take 12 = xt and substitute into the first,  and then we have

12 = x - 12 + 7 - 7t

12 = x - 5 - 7t

0= x - 7t - 17; now we will substitute  t = 12/x and we get

0 = x - 84/x - 17.  We multiply all terms by x and finally we get this quadratic equation:

x² - 17x - 84 = 0.

 

Solve this by factoring; the only valid answer is x=21 -- the rate in mph of the homebound part of the trip.

 

Check the answer on both trips!