Two buses start at the same point and travel in opposite directions. The first bus travels 10 miles per hour faster than the second bus. In 3 hours, the buses are 282 miles apart. Use the formula below to determine the rate of the second bus.

Question

3(r + 10) + 3r = 282

Answer 1

Let's solve the equation given in the problem step by step.

The equation provided is:

\[ 3(r + 10) + 3r = 282 \]

1. Distribute the 3 on the left side:

\[ 3r + 30 + 3r = 282 \]

2. Combine like terms:

\[ 6r + 30 = 282 \]

3. Subtract 30 from both sides:

\[ 6r = 282 - 30 \]

\[ 6r = 252 \]

4. Now, divide both sides by 6:

\[ r = \frac{252}{6} \]

\[ r = 42 \]

So, the rate of the second bus is 42 miles per hour.

To confirm, we can determine the rate of the first bus, which is \( r + 10 = 42 + 10 = 52 \) miles per hour. In 3 hours, the first bus travels:

\[ 3 \times 52 = 156 \text{ miles} \]

And the second bus travels:

\[ 3 \times 42 = 126 \text{ miles} \]

Adding these distances gives:

\[ 156 + 126 = 282 \text{ miles} \]

This checks out, confirming that the rate of the second bus is indeed 42 miles per hour.