Distance Formula Word Problem

by Chuck
(Corning Ny)

A cattle train left Miami and traveled toward New York. 14 hours later a diesel train left traveling at 45 km/h in an effort to catch up to the cattle train. After traveling for four hours the diesel train finally caught up. What was the cattle train's average speed?

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Distance Formula Word Problem

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Jun 22, 2010
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by: Karin

Hi Chuck,

This is an interesting problem. Again, we are going to use the distance formula since we have information about rate and time.

The distance formula is: Distance = rate * time

We know more information about the diesel train, so let's start there.

It took 4 hours for the diesel train to catch up with the cattle train, so time is 4 hours. Rate of 45 km/h was given. So, with this information we can find the distance.

D = rt
D = 45 * 4
D = 180 km.

The distance was 180 km and since the diesel train caught up with the cattle train, the distance is the same for both trains.

So, now for the cattle train, we know that the distance is 180 km (same as diesel train) and we know that the time to get that distance is 18 hours. It's eighteen hours because the cattle train started 14 hours before the diesel train, plus the 4 hours that it took for the diesel train to meet up with the cattle train.

So, again we can use the distance formula to find the rate of the cattle train.

D = rt
180 km = r(18)

18r = 180 Switch the problem around
18r/18 = 180/18 Divide by 18
r = 10 km/h

The rate of the cattle train was 10 km/h

I hope this helps.

Karin

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