SOLUTION: The highway distance between two cities is 280 miles. The speed for 80 miles of the trip from one city to the other is 10 mph faster than the speed for the remainder of the distanc

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Question 883478: The highway distance between two cities is 280 miles. The speed for 80 miles of the trip from one city to the other is 10 mph faster than the speed for the remainder of the distance. Find the two speeds if the total time of the trip is 6 hours?
Answer by lwsshak3(11628) About Me  (Show Source):
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The highway distance between two cities is 280 miles. The speed for 80 miles of the trip from one city to the other is 10 mph faster than the speed for the remainder of the distance. Find the two speeds if the total time of the trip is 6 hours?
***
let x=speed for 80 miles of the trip
x-10=speed for remaining 200 miles of the trip
travel time=distance/speed
..
80%2Fx%2B200%2F%28x-10%29=6
lcd=x(x-10)
80(x-10)+200x=6x(x-10)
80x-800+200x=6x^2-60x
6x^2-340x+800
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=6, b=-340, c=800
ans:
x≈2.5(reject, not reasonable)
or
x≈54.2
x-10≈44.2
speed for 80 miles of the trip=54.2 mph
speed for remaining 200 miles of the trip=44.2 mph