SOLUTION: (((A cyclist traveled at a rate of 32 MPH to visit a nearby town. The cyclist averaged 10 MPH on the return trip. If the round trip took 6.3 hours, find the distance to the nearb

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Question 224310: (((A cyclist traveled at a rate of 32 MPH to visit a nearby town. The cyclist averaged 10 MPH on the return trip. If the round trip took 6.3 hours, find the distance to the nearby town.)))
I have tried and tried to come up with an equation for this word problem but I cannot come up with one. I have found the answer which is 48 miles to the nearby town. But I need the equation and I am not sure how to get to it.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A cyclist traveled at a rate of 32 MPH to visit a nearby town. The cyclist averaged 10 MPH on the return trip. If the round trip took 6.3 hours, find the distance to the nearby town.
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To-town DATA:
rate = 32 mph ; distance = x miles ; time = d/r = x/32 hrs
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From-town DATA:
rate = 22 mph ; distance = x miles ; time = d/r = x/22 hrs
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Equation:
time + time = 6.3 hrs
x/32 + x/22 = 6.3 hrs
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Multiply thru by 32*22 to get:
22x + 32x = 22*32*6.3
54x = 4435.2
x = 82.13.. miles (distance to the town)
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Cheers,
Stan H.