Question

train A and train B leave a central station at the same time. they travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. train A reaches station A after 4 h. train B reaches station B after 3 1/2 h. station A and B are 562.5 mi apart. What are the rate of the trains?

Answer 1

The rate of the trains are 75 mph.

Explanation:

Consider the provided information.

Train A and train B leave a central station at the same time with same speed, but in opposite directions.

Train A reaches station A after 4 h. train B reaches station B after 3 1/2 h.

The total time taken by train A and train B is:

`4+3(1)/(2)`

`4+(7)/(2)`

`(8+7)/(2)`

`7.5}`

Thus, the total time taken is 7.5 hrs.

It is given that station A and B are 562.5 mi apart.

That means both the trains cover 562.5 mi in 7.5hr

As we know: Rate = distance / time or Speed = distance / time

Here, rate and speed are the same thing.

Now substitute the respective values in the above formula.

`Rate=(562.5)/(7.5)`

`Rate=75`

Hence, the rate of the trains are 75 mph.