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 truc
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Question 1085092: 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) Found 2 solutions by ikleyn, jorel1380:Answer by ikleyn(52832) (Show Source):
Let "t" be the average speed of the truck, in mph.
Then the average speed of the car is (t+10) mph.
Then your "total combined time equation" is
= 12.
Indeed, is the time for the truck to cover 378 miles, while is the time for the car to cover 320 miles.
To solve the equation, multiply both sides by t*(t+10). You will get
378*(t+10) + 320t = 12t*(t+10).
Simplify and solve this quadratic equation by any method you know.
Answer. The average speed of the truck is 54 mph. The average speed of the car is 64 mph.
Check. + = 7 + 5 = 12. Correct !!
You can put this solution on YOUR website! Let s and s+10 be the speeds of the truck and the car, respectively. Then:
378/s + 320/s+10=12
378(s+10)+320s=12(sē+10s)
378s+3780+320s=12sē+120s
12sē-578s-3780=0
6sē-289s-1890=0
Using the quadratic formula, we get roots of 54 and -5.833333, so we use 54 mph as the positive speed of the truck.
Also:
(6s+35)(s-54)=0 also gives us roots of 54 and -5.8333333. ☺☺☺☺
