Question

Two trains leave a station at the same time. One train is heading south at a rate that is 1.5 times faster than the other train, which is heading north. After 5 hours, the trains are 750 miles apart.
1) At what speed, in mph, are the two trains getting farther away from each other?
2) What is the speed, in mph, of the faster train?
3) Suppose the trains simultaneously leave stations that are 450 miles apart and travel toward each other. In how many hours will the trains meet?

Answer 1

Based on the data given, the speeds and time taken are as follows:

1. The combined speed of the two trains is 150 mph
2. The speed of faster train 150 x 3/5 = 90 mph
3. The time taken by the trains to cover 450 miles = 3 hours

What is speed?

Speed is the ratio of distance covered and time taken.

• Speed = distance/time

1)The distance covered by the two trains in 5 hours = 750 miles.

The trains move at a constant speed and their combined speed will be:

Combined speed = 750/5

Combined speed = 150 mph

2) The train heading south has a speed 1.5 times faster than the other train heading north.

Ratio of speeds = 3 : 2

Speed of faster train 150 x 3/5 = 90 mph

3) The combined speed of the trains = 150 mph

Distance to be covered = 450 miles

Time taken = 450/150

Time taken = 3 hours

In conclusion, the speed of the two trains are determined from the distance travelled and time taken.

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Answer 2

Answer:

1) 150 mph

2) 90 mph

3) 3 mph

Explanation:

1) The trains move at a constant speed, and after 5 hours they are 750 miles apart. 750/5=150

2) The faster train is 1.5 faster than the slower train, and we know their combined speed is 150 mph. 150/5=30, and 30x3=90.

3) We know that both trains combined travel 150 mph. 450/150=3.