Rate of trains

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 312 h. Station A and Station B are 562.5 mi apart.

What is the rate of the trains?

Answer 1

Hi Mia, 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:

 

d_a = R * 4

 

Train B:

 

d_b = 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.

 

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