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You are here: Experts > Science > Math for Kids > Word Problems > Uniform Motion Problem
Expert: Scott A Wilson - 10/29/2009
Question
a car and a bus set out at 2 p.m. from the same point headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In 2 h the car is 20 mi ahead of the bus. Find the rate of the car.
Answer
Let C = car spped and B = bus speed. It is known that C+30=2B.
Distance in 2 hours is 2C and 2B.
It is also known that C+30=2B.
After 2 hours have passed, car C is 20 miles ahead, so 2C = 2B + 20.
We already have 2B=C+30, so putting 2B in gives us 2C = (C+30) + 20.
This works out to 2C = C + 50. Subtracting C from both sides gives C = 50.
Now if C=50, 50+30=2B => 80=2B => B=40.
After 2 hours have passed, the car has gone 100 miles and the bus has gone 80.
100-80=20, and that is how far is suppoes to be between them, so the answer has been checked.
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