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.

Question

What is the rate of the trains?



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Answer 1

To determine the rate of the trains, we can use the distance formula:

\[ \text{Distance} = \text{Rate} \times \text{Time} \]

From the information given:

1. Train A travels for 4 hours to reach Station A.
2. Train B travels for 312 hours to reach Station B.

Since both trains travel at the same speed, we can denote their common speed as \( r \) (in miles per hour).

For Train A: \[ \text{Distance to Station A} = r \times 4 \]

For Train B: \[ \text{Distance to Station B} = r \times 312 \]

Since the total distance between Station A and Station B is 562.5 miles, we can write the equation:

\[ r \times 4 + r \times 312 = 562.5 \]

This simplifies to:

\[ 4r + 312r = 562.5 \]

Combining the terms gives:

\[ 316r = 562.5 \]

Now, we can solve for \( r \):

\[ r = \frac{562.5}{316} \]

Calculating this:

\[ r \approx 1.78 \text{ miles per hour} \]

Thus, the rate of the trains is approximately:

\[ \boxed{1.78} \] (miles per hour)