Question

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 = 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.