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 given to determine the rate of the second bus.
3(r+10)+3r = 282
A. R = 42 mph
B. R = 30mph
C. R =45mph
D. R = 21 mph
3(r+10)+3r = 282
A. R = 42 mph
B. R = 30mph
C. R =45mph
D. R = 21 mph
Answers
GPT-4o mini
To solve for the rate of the second bus, we start from the equation given:
\[
3(r + 10) + 3r = 282
\]
where \( r \) is the rate of the second bus in miles per hour.
First, we can simplify the equation:
\[
3r + 30 + 3r = 282
\]
Combine like terms:
\[
6r + 30 = 282
\]
Now, we can isolate \( 6r \) by subtracting 30 from both sides:
\[
6r = 282 - 30
\]
\[
6r = 252
\]
Next, divide both sides by 6:
\[
r = \frac{252}{6}
\]
\[
r = 42
\]
Thus, the rate of the second bus is \( r = 42 \) mph.
The correct answer is:
**A. R = 42 mph**
\[
3(r + 10) + 3r = 282
\]
where \( r \) is the rate of the second bus in miles per hour.
First, we can simplify the equation:
\[
3r + 30 + 3r = 282
\]
Combine like terms:
\[
6r + 30 = 282
\]
Now, we can isolate \( 6r \) by subtracting 30 from both sides:
\[
6r = 282 - 30
\]
\[
6r = 252
\]
Next, divide both sides by 6:
\[
r = \frac{252}{6}
\]
\[
r = 42
\]
Thus, the rate of the second bus is \( r = 42 \) mph.
The correct answer is:
**A. R = 42 mph**