SOLUTION: The total combined time for a truck to travel 378 miles and a car to travel 320 miles is 12 hours. If the average speed of the car is 10 mph more than the average speed of the tru

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Question 758185: The total combined time for a truck to travel 378 miles and a car to travel 320 miles is 12 hours. If the average speed of the car is 10 mph more than the average speed of the truck, find the average speed of the truck. (use the quadratic formula to solve this problem).
Answer by lwsshak3(11628) About Me  (Show Source):
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The total combined time for a truck to travel 378 miles and a car to travel 320 miles is 12 hours. If the average speed of the car is 10 mph more than the average speed of the truck, find the average speed of the truck
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let x=speed of truck
x+10=speed of car
travel time=distance/speed
..
378%2Fx%2B320%2F%28x%2B10%29=12
378%28x%2B10%29%2B320x=12%2Ax%28x%2B10%29
378x%2B3780%2B320x=12x%5E2%2B120x%29
12x^2-578x-3780=0
6x^2-289x-1890=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=6, b=-289, c=-1890
x+=+%28289+%2B-+sqrt%28+83521%2B45360+%29%29%2F%2812%29+
x+=+%28289+%2B-+sqrt%28+128881+%29%29%2F%2812%29+
x = (289 ±359)/(12)
x=54
or
x=-5.83(reject, x>0)
speed of truck=54 mph
x+10=speed of car=64 mph