Question

LOTS OF POINTS, PLEASE ANSWER

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 Station B are 562.5 mi apart.

What are the rates of the trains?

Answer 1

speed = distance / time

since they are moving in opposite direction, the time is the sum of the two times = 2 1/2 + 4 = 6 1/2 = 13/2

speed = 585/(13/2) = 90 miles per hour.

Explanation:

I hope it helps.

Answer 2

since the rate is the same for both trains, and we know that the distance train A travels plus the distance train B travels equals 562.5 miles, we can use the D(istance) = R(ate) * T(ime) formula to solve this.

Train A:

da = R * 4

Train B:

db = R * 3.5 (using 3.5 instead of 3 and 1/2)

Solve for R:

R * 4 + R * 3.5 = 562.5

7.5 * R = 562.5

R = 75

The trains are traveling at 75 miles per hour.

Explanation: