Answer:
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
