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 = [tex]\frac{510}{u} +\frac{510}{u-25}[/tex]
Equating both times we have
[tex]\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[/tex]
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
