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

Answer 1

We can solve the equation \(3(r + 10) + 3r = 282\) step by step.

1. Distribute \(3\) to both terms inside the parentheses: \[ 3r + 30 + 3r = 282 \]

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

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

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

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

To verify, we can calculate the rate of the first bus, which is \( r + 10 = 42 + 10 = 52\) miles per hour.

In 3 hours, the distances traveled by both buses will be:

• Distance by the second bus: \(3r = 3 \times 42 = 126\) miles
• Distance by the first bus: \(3(r + 10) = 3 \times 52 = 156\) miles

Adding the two distances together: \[ 126 + 156 = 282 \text{ miles} \]

This confirms that the calculations are correct. The rate of the second bus is indeed \( \boxed{42} \) miles per hour.