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 312 h. station a and station b are 562.5 mi apart.
what is the rate of the trains?
it is very important

The rate of the trains is 75 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- Trains A and B leave the central station at the same time

- They travel with the same speed

* Assume that their speed is x miles/hour

- They travel in opposite direction, Train A towards station A and train

  B towards station B

- Train A reaches station A after 4 hours

* Train A travels for 4 hours

- Train B reaches station B after 3 1/2 hours

* Train B travels for 3 1/2 hours

- Station A and Station B are 562.5 mi apart

* The total distance that the two trains travel is 562.5 miles

- Lets solve the problem

∵ Distance = speed × time

# For train A

∵ Its speed is x miles/hour

∵ Its time is 4 hours

∴ Its distance D(A) = 4 × x = 4 x miles

# For train B

∵ Its speed is x miles/hour

∵ Its time is 3 1/2 hours

∴ Its distance D(B) = 3 1/2 × x = 3.5 x miles

∵ The total distance is 562.5 miles

∴ D(A) + D(B) = 562.5

∴ 4 x + 3.5 x = 562.5

∴ 7.5 x = 562.5

- Divide both sides by 7.5

∴ x = 75

∵ x represents the speed of the trains

∴ The rate of the trains is 75 miles per hour