SOLUTION: I need help with this word problem. It seems easy at first, but the answer that I got was denied by my math teacher. He said it's supposed to be harder than that. So here it go

Question 135: I need help with this word problem. It seems easy at first, but the answer that I got was denied by my math teacher. He said it's supposed to be harder than that. So here it goes:
A man is traveling up a hill at 30 mph and immediately returns down. His average speed for the whole trip is 45 mph. What is the man's speed going down the hill?
At first, I thought it was 60 mph, but my algebra teacher said it was wrong. Is it because the word problem does not say how long it took the man to travel up and down the hill? My algebra teacher said that the question was answerable, so please help me out. Thank you.
Katie, 14
Answer by ichudov(499) (Show Source):
You can put this solution on YOUR website!
The time it took the man to travel uphill is:
time to travel uphill = distance/30 mph
time to travel downhill = distance/downhill speed
Average speed is the total distance (which is twice the distance to go one way), divided by total time:

we know that average_speed is 45:

Simplifying

distance cancels out (and that's why it was not given in the problem):

45*downhill_speed+30*45 = 60*downhill_speed
15*downhill_speed = 30*45
downhill_speed = 30*3 = 90