SOLUTION: A bus traveled 180 miles. If weather conditions had been better, it could have driven 5 miles an hour faster and completed the trip in 30 minutes less time. How fast did the bus

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Question 357658: A bus traveled 180 miles. If weather conditions had been better, it could have driven 5 miles an hour faster and completed the trip in 30 minutes less time. How fast did the bus travel?
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A bus traveled 180 miles. If weather conditions had been better, it could have driven 5 miles an hour faster and completed the trip in 30 minutes less time. How fast did the bus travel?
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Old speed data:
distance = 180 ; rate = x mph ; time = 180/x hrs
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New speed data:
distance = 180 miles ; rate = x+5 mph ; time = 180/(x+5) hrs
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Equation:---
old time - new time = 1/2 hr
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180/x - 180/(x+5) = 1/2
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Multiply thru by 2x(x+5) to get:
180*2(x+5) - 180*2x = x(x+5)
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360x + 5*360 - 360x = x^2+5x
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x^2+5x-1800 = 0
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(x-40)(x+45) = 0
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x = 40 mph
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Cheers,
Stan H.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
180%2Fr+-+180%2F%28r%2B5%29+=+1%2F2,
180%281%2Fr-1%2F%28r%2B5%29%29+=+1%2F2,
360%2A%285%2F%28r%28r%2B5%29%29%29+=+1,
1800+=+r%5E2%2B5r,
r%5E2%2B5r-1800=0,
%28r-40%29%28r%2B45%29+=+0,
Therefore r = 40 miles per hour.