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 given to determine the rate of the second bus.

3(r+10)+3r = 282
A. R = 42 mph
B. R = 30mph
C. R =45mph
D. R = 21 mph

1 answer

To solve for the rate of the second bus, we start from the equation given:

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

where \( r \) is the rate of the second bus in miles per hour.

First, we can simplify the equation:

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

Combine like terms:

\[ 6r + 30 = 282 \]

Now, we can isolate \( 6r \) by subtracting 30 from both sides:

\[ 6r = 282 - 30 \]

\[ 6r = 252 \]

Next, divide both sides by 6:

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

\[ r = 42 \]

Thus, the rate of the second bus is \( r = 42 \) mph.

The correct answer is:

A. R = 42 mph