To determine the rate of the second bus, we can start by analyzing the given equation and the information provided.
Let \( r \) be the rate of the second bus in miles per hour. Then, the rate of the first bus is \( r + 10 \) miles per hour.
After traveling for 3 hours, the distance each bus has traveled can be expressed as follows:
- Distance traveled by the second bus = \( 3r \)
- Distance traveled by the first bus = \( 3(r + 10) \)
According to the problem, the total distance between the two buses is 282 miles. We can set up the equation:
\[ 3(r + 10) + 3r = 282 \]
Now, we can simplify and solve the equation:
\[ 3(r + 10) + 3r = 282 \]
Expanding the left side:
\[ 3r + 30 + 3r = 282 \]
Combining like terms:
\[ 6r + 30 = 282 \]
Subtracting 30 from both sides:
\[ 6r = 252 \]
Dividing both sides by 6:
\[ r = 42 \text{ mph} \]
Thus, the rate of the second bus is 42 mph.
The correct answer from the options provided is r = 42 mph.
1 answer