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 = 30 mph
r = 30 mph

r = 45 mph
r = 45 mph

r = 21 mph
r = 21 mph

r = 42 mph
r = 42 mph

Answer 1

Let's analyze the equation given:

The first bus travels at a speed of \( r + 10 \) mph (10 miles per hour faster than the second bus), and the second bus travels at \( r \) mph. Both buses travel for 3 hours, and the total distance they cover is 282 miles apart.

Using the distance formula, we can express the distances traveled by each bus:

• Distance traveled by the first bus in 3 hours: \( 3(r + 10) \)
• Distance traveled by the second bus in 3 hours: \( 3r \)

Setting up the equation based on the total distance:

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

Now, let's simplify this equation.

1. Distribute the 3: \[ 3r + 30 + 3r = 282 \]

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, \( r \), is \( 42 \) mph.

The correct response is:

r = 42 mph