SOLUTION: A car travels 15 kilometers per hour faster than a truck. The car goes 360 kilometers in 2 hours less time than it takes the truck to travel the same distance. Find the speed of th
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Question 102667: A car travels 15 kilometers per hour faster than a truck. The car goes 360 kilometers in 2 hours less time than it takes the truck to travel the same distance. Find the speed of the truck and the car.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
car travels 15 kilometers per hour faster than a truck. The car goes 360 kilometers in 2 hours less time than it takes the truck to travel the same distance. Find the speed of the truck and the car.
:
Let s = speed of the truck
then
(s + 15) = speed of the car
:
Write a time equation: Time = Distance/speed
:
Truck time - car time = 2 hrs
- = 2
:
Multiply equation by s(s+15) to get rid of the denominator, results:
360(s+15) - 360s = 2(s(s+15)
:
360s + 5400 - 360s = 2(s^2 + 15s)
:
5400 = 2(s^2 + 15s)
:
Simplify, divide both sides by 2
2700 = s^2 + 15s
:
s^2 + 15s - 2700 = 0; a quadratic equation
:
Factors to:
(s + 60) (s - 45) = 0
:
s = +45 mph is the truck (positive solution)
:
45 + 15 = 60 mph is the car
:
:
Check solution by finding the time of each:
360/45 = 8 hrs
360/60 = 6 hrs
---------------
difers = 2 hrs as given in the problems
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