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# Trains that pass in the night

## Question

If it takes the 10-car Silver Streak passenger train twice as long* to pass the 93-car Big Boy steam freight train going in the same direction as it does going the opposite direction, what is the ratio of their speeds?

*Meaning the time during which there is any overlap of the trains.

## Recommended Posts

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Spoiler

Distance = Speed * Time

If we let one train's speed be relative to the other, we just need to set the two Speed*Time values equal to each other.  Both of which will equal the sum of the lengths of the two trains, but since we don't need to calculate it the number of cars in each train is a red herring.

2T(S-RS) = D = T(S+RS)

2TS(1-R) = TS(1+R)

2(1-R) = (1+R)

2-2R = 1+R

1 = 3R

1/3 = R

The Silver Streak passenger train is moving three times the speed of the other.  So the ratio is 3:1.

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