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
A) r = 30 mph
B) r = 21 mph
C) r = 45 mph
D) r = 42 mph

Answer 1

To solve for the rate of the second bus using the equation provided, we start with:

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

First, we can simplify the equation:

1. Distribute \(3\) to both terms inside the brackets: \[ 3(r + 10) = 3r + 30 \]

2. Substitute back into the equation: \[ 3r + 30 + 3r = 282 \]

3. Combine like terms: \[ 6r + 30 = 282 \]

4. Subtract \(30\) from both sides: \[ 6r = 252 \]

5. Divide both sides by \(6\): \[ r = 42 \]

So, the rate of the second bus is \(42\) mph.

The correct answer is: D) r = 42 mph.