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

(1 point)
Responses

r = 21 mph
r = 21 mph

r = 42 mph
r = 42 mph

r = 45 mph
r = 45 mph

r = 30 mph

Answer 1

To find the rate of the second bus, we can solve the equation that has been given:

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

This equation represents the distance traveled by both buses in 3 hours. The first bus travels at a speed of \( r + 10 \) (10 mph faster than the second bus), and the second bus travels at a speed of \( r \).

Let's simplify the equation:

1. Distribute the 3: \[ 3(r + 10) + 3r = 282 \] becomes \[ 3r + 30 + 3r = 282 \]

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

3. Subtract 30 from both sides: \[ 6r = 252 \]

4. Divide by 6: \[ r = 42 \]

Thus, the rate of the second bus is \( \boxed{42} \) mph.