SOLUTION: Mr. Brown drove from his home to his school at the rate of 25 mph and returned by a different route at the rate of 30 mph. The route by which he returned was 5 miles longer than th

Question 1106450: Mr. Brown drove from his home to his school at the rate of 25 mph and returned by a different route at the rate of 30 mph. The route by which he returned was 5 miles longer than the route by which he went. The return trip took 10 minutes less than the trip out. Find the distance Mr. Brown traveled each way.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mr. Brown drove from his home to his school at the rate of 25 mph and
returned by a different route at the rate of 30 mph.
The route by which he returned was 5 miles longer than the route by which he went.
The return trip took 10 minutes less than the trip out.
Find the distance Mr. Brown traveled each way.
:
let t = travel time at 25 mph
10 min = 1/6 hr, therefore
(t-) = time at 30 mph
:
write a distance equation; dist = speed * time
return dist = to dist + 5 mi
30(t-) = 25t + 5
30t - 5 = 25t + 5
30t - 25t = 5 + 5
5t = 10
t = 10/5
t = 2 hrs is the travel time at 25 mph
therefore
25 * 2 = 50 mi to school
and
50 + 5 = 55 mi return home
:
:
Check solution by finding the return dist
30(2-)
30(1) = 55 mi

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