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?

Answer:The rate of the trains is 75 miles per hourStep-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