SOLUTION: five friends drove at an average rate of 50 miles per hour to a weekend retreat. On the way home, they took the same route but averaged 75 miles per hour. What was the distance bet

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Question 182256: five friends drove at an average rate of 50 miles per hour to a weekend retreat. On the way home, they took the same route but averaged 75 miles per hour. What was the distance between home and the retreat if the round trip took 10 hours?
Found 3 solutions by stanbon, rapaljer, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
five friends drove at an average rate of 50 miles per hour to a weekend retreat. On the way home, they took the same route but averaged 75 miles per hour. What was the distance between home and the retreat if the round trip took 10 hours?
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To the retreat DATA:
rate = 50 mph ; distance = x miles : time = d/r = x/50 hrs
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From the retreat DATA:
rate = 75 mph ; distance = x miles ; time = d/r = x/75 hrs
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Equation:
x/50 + x/75 = 10
75x + 50x = 50*75*10
125x = 50*75*10
x = 300 miles
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Cheers,
Stan H.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = time it takes to get TO the retreat.
Then 10-t = time it takes to get BACK from the retreat.

Distance to the retreat = Distance back from the retreat
Rate * Time = Rate * Time
50*t = 75(10-t)
50t = 750 -75t
50t+75t = 750
125t=750
t=6 hours to get TO the retreat at 50 mph = 300 miles

As a check, this means that it took only 4 hours to return at 75 mph.
4*75 = 300 miles, and it checks!!

R^2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let the time to travel to the retreat be t hours, then the time to return from the retreat must be 10 - t.

Knowing that distance equals rate times time:



We can write, for the trip to the retreat:



And for the return trip:



But since the distances are equal, we can write:



Solve this equation for t and then substitute this value in:



to get the required distance.

John