SOLUTION: During the first part of a trip, a car travels 50 miles at a certain speed. It then travels 80 miles on the second part at a speed 10 mph slower than the first part. The total time

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Question 600278: During the first part of a trip, a car travels 50 miles at a certain speed. It then travels 80 miles on the second part at a speed 10 mph slower than the first part. The total time from the trip is 3 hours. What is the speed on each part of the trip?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
During the first part of a trip, a car travels 50 miles at a certain speed. It then travels 80 miles on the second part at a speed 10 mph slower than the first part. The total time from the trip is 3 hours. What is the speed on each part of the trip?
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1st part DATA:
distance = 50 miles ; rate = x mph / time = d/r = 50/x hrs
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2nd part DATA:
distance = 80 miles ; rate = (x-10) mph ; time = d/r = 80/(x-10) hrs
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Equation:
time + time = 3 hrs
50/x + 80/(x-10) = 3 hrs
50(x-10) + 80x = 3x(x-10)
50x-500 + 80x = 3x^2-30x
3x^2-80x + 500 = 0
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Usable answer:
x = 16 2/3 mph (1st part rate)
x-10 = 6 3/4 mph (2nd part rate)
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Cheers,
Stan H.
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