SOLUTION: An experimental electric-solar car completed a 1000-mi. race in 35 hrs. For the 600 mi. traveled during daylight the car averaged 20 mph more than it did for the 400 mi. traveled

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Question 70377: An experimental electric-solar car completed a 1000-mi. race in 35 hrs. For the 600 mi. traveled during daylight the car averaged 20 mph more than it did for the 400 mi. traveled at night. What is the average speed of the car during the daytime?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An experimental electric-solar car completed a 1000-mi. race in 35 hrs. For the 600 mi. traveled during daylight the car averaged 20 mph more than it did for the 400 mi. traveled at night. What is the average speed of the car during the daytime?
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Night travel DATA:
distance = 400 mi, rate = x mph ; time = d/r = 400/x hrs
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Day travel DATA:
distance = 600 mi ; rate = x+20 mph; time = d/r = 600/(x+20)
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EQUATION:
time + time = 35 hrs
400/x + 600/(x+20) = 35
Divide thru by 5 to get smaller numbers:
80/x + 120/(x+20) = 7
[80(x+20) + 120x] = 7x(x+20)
200x +1600 = 7x^2 + 140x
7x^2 -60x -1600 = 0
(x-20)(7x+80)=0
x=20 mph (rate during the night
x+20= 40 mph (rate during the day)
Cheers,
Stan H.