SOLUTION: I am stumped by this question: Michael drove to a friend's house at a rate of 40 mph. He returned by the same route at a rate of 45 mph. The driving time for the round trip w

Question 484184: I am stumped by this question:
Michael drove to a friend's house at a rate of 40 mph. He returned by the same route at a rate of 45 mph. The driving time for the round trip was 4 hours. What is the distance Michael traveled.
I came up with ((40+45)/2)*4 = 170
I don't think that is the right answer because it assumes I traveled 2 hours at each speed which doesn't seem correct. Can you advise what the correct formula is to solve this problem?
Thanks.
Found 2 solutions by Alan3354, chessace:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Michael drove to a friend's house at a rate of 40 mph. He returned by the same route at a rate of 45 mph. The driving time for the round trip was 4 hours. What is the distance Michael traveled.
--------------
d/40 + d/45 = 4
45d + 40d = 7200
d = 7200/85 miles
d = 1440/17 miles
------------------
The avg speed for the round-trip is 2*40*45/(40+45)
= 42.353 mph
It's less than the average of 40 & 45 because more time is spent going slower.

Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
Your doubt is correct.
As always, make x = what is asked for, the total distance.
Speed = Distance / time.
So Time = Distance / speed.
The trip out will take (time T) = (dist x/2) / (speed 40)
The trip back will take (time T) = (dist x/2) / (speed 45)
Total time: + = 4
Solve for x:
mult by 2 * 5:
mult by 72:
Div by 17: x = 169.4 miles.
Note that your attempt is an excellent "reasonable" test.
It is off by only 10 football fields.

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