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.