Question 836132: A train is moving along a straight stretch of track parallel to a highway. An automobile travelling 60 miles an hour in the same direction as the train can pass it in 30 seconds. Travelling in the opposite direction the automobile requires only 7 ½ seconds to passed the train. How long is the train and how fast is it moving? (Neglect the length of the auto mobile.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! believe the solution is:
the train is moving at 52.8 feet per second and the length of the train is 1056 feet.
here's how i determined that.
60 miles per hour is equal to 60 * 5280 feet per hour which is equal to 31,800 feet per hour.
divide that by 3600 and you get 88 feet per second.
the car is traveling at 88 feet per second.
in 30 seconds, the car has traveled 30 * 88 feet which is equal to 2640 feet.
in 7.5 seconds, the car has traveled 7.5 * 88 feet which is equal to 660 feet.
when the car is traveling in the same direction as the train, the car has traveled 2640 feet, but the train has traveled 2640 - X feet.
the formula for the rate of speed of the train becomes:
30 * R = 2640 - X
when the car is traveling in the opposite direction as the train, the car has traveled 660 feet, but the train has traveled 660 + X feet.
the formula for the rate of speed of the train becomes:
7.5 * R = 660 + X
if we solve for X in each of these equations, we will get:
X = 2640 - 30 * R
X = 660 + 7.5 * R
since both expressions on the right side of these equations are equal to X, we can set these expressions equal to each other to get.
2640 - 30 * R = 660 + 7.5 * R
if we solve for R, we will get:
37.5 * R = 1980
if we divide both sides of this equation by 37.5, we will get:
R = 52.8
the train is traveling at 52.8 feet per second.
in 30 seconds, the train has traveled 30 * 52.8 = 1584 feet.
since the car has traveled 2640 feet, the length of the train has to be 2640 - 1584 = 1056 feet.
in 7.5 seconds, the train has traveled 7.5 * 52.8 = 396 feet.
since the car has traveled 660 feet, the length of the train has to be 396 + 660 = 1056 feet.
so the length of the train is 56 feet.
the speed of the train is 52.8 feet per second.
multiply this by 3600 and divide it by 5280 to get the speed of the train is 36 miles per hour.
that should be your answer.
a picture of what this looks like is shown below:
when the car is traveling in the same direction as the train, it starts at the back of the train and ends up at the front of the train.
when the car is traveling in the opposite direction as the train, it starts at the front of the train and ends up at the back of the train.
when the train is traveling in the same direction as the train, the length of the train is determined by taking the total distance the car has traveled and subtracting the the total distance the train has traveled.
when the train is traveling in the opposite direction as the train, the length of the train is determined by taking the total distance the car has traveled and adding the total distance the train has traveled.
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