Question

Jamie recently drove to visit her parents who live 510 miles away. On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of 17 hours driving, find the two rates.

Answer 1

Answer:

       Average speed in mph with which he goes to parent's place = 75 mph

       Average speed with he comes back = 50 mph

Explanation:

  Distance between Jamie's house and parent's house = 510 miles.

  Let u be the average speed in mph with which he goes to their place.

  We have the average speed of coming back = (u -25) mph

  Total time of journey considering both ways = 17 hours.

  Time taken to go their home = 510/u hours

  Time taken for coming back = 510/(u-25) hours

  So total time = $\frac{510}{u} +\frac{510}{u-25}$

 Equating both times we have

       $\frac{510}{u} +\frac{510}{u-25}=17\\ \\ 510u-12750+510u=17u^2-425u\\ \\ 17u^2-1445u+12750=0\\ \\ u^2-85u+750=0\\ \\ (u-75)(u-10)=0$

  u = 75 mph or u =10 mph

If the average speed in mph with which he goes to their place = 75 mph, average speed with he comes back = 75-25 = 50 mph

If the average speed in mph with which he goes to their place = 75 mph, average speed with he comes back = 10-25 = -15 mph(Not possible)

So,  Average speed in mph with which he goes to parent's place = 75 mph

       Average speed with he comes back = 50 mph