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 = 45 mph
r = 45 mph

r = 30 mph
r = 30 mph

r = 42 mph
r = 42 mph

r = 21 mph

Answer 1

To find the rate of the second bus, we start with the equation given:

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

First, distribute the 3 to both terms in the first part of the equation:

\[ 3r + 30 + 3r = 282 \]

Combine like terms:

\[ 6r + 30 = 282 \]

Next, subtract 30 from both sides:

\[ 6r = 252 \]

Now, divide both sides by 6 to solve for \( r \):

\[ r = 42 \]

Therefore, the rate of the second bus is

\[ \boxed{42 \text{ mph}} \]