SOLUTION: A car and a train leave station A at the same time for station B, 300 miles away. If the speed of the car averages twice the speed of the train and the car arrives 7.5 hours before

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Question 130928: A car and a train leave station A at the same time for station B, 300 miles away. If the speed of the car averages twice the speed of the train and the car arrives 7.5 hours before the train, find the speed of the car and the speed of the train in miles per hour.
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Solution -
Let the speed of the car be x miles/hour
and the speed of train be y miles/hour
According to first condition
that is speed of the car is twice the speed of the train
x = 2y ..... (i)
According to the second condition
time taken by car to cover 300 miles = distance/speed
= 300/x
time taken by train to cover 300 miles = 300/y
now car arrives 7.5 hours before train
therefore
300/x + 7.5 = 300/y (since train takes 7.5 hours more than car therefore we will add 7.5 hours with the time of the car to equate the value)
now substituting the value of x from equation (i) we have
300/2y +7.5 = 300/y
now transfering the like terms on one side we have
7.5 = 300/y - 300/2y
75/10 = (600 - 300)/2y
75/10 = 300/2y
15/2 = 150/y
now by cross multiplicationb we have
15y = 300
y = 300/15
y = 20
now substituting the value of y in equation (i) we have
x = 2y
x = 2*20
x = 40
therefore the speed of the train is y miles/hour = 20 miles/hour
and speed of car is x miles/hour = 40 miles/hour

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