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. 3(r + 10) + 3r = 282 (1 point) Responses r = 30 mph r = 30 mph r = 45 mph r = 45 mph r = 42 mph r = 42 mph r = 21 mph r = 21 mph

Answer 1

To solve for the rate of the second bus (\(r\)), we can use the equation provided:

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

First, simplify the equation:

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

Combine like terms:

\[ 6r + 30 = 282 \]

Next, subtract 30 from both sides:

\[ 6r = 252 \]

Now, divide both sides by 6:

\[ r = 42 \]

So, the rate of the second bus is \( \text{r = 42 mph} \).

The correct response is:

r = 42 mph