Question

Melanie’s family drove for 5 hours on the main highway and 3 hours on a smaller highway, and traveled a total of 456 miles. Their average speed was 8 miles per hour faster on the main highway than on the smaller highway. What was their average speed on the smaller highway?

A.
57 miles per hour


B.
49 miles per hour


C.
52 miles per hour


D.
53 miles per hour

Answer 1

Let the average speed on the smaller highway be \( x \) miles per hour. Then, the average speed on the main highway would be \( x + 8 \) miles per hour.

Now we can calculate the distances covered on each highway:

1. Distance traveled on the main highway (5 hours):
\[
\text{Distance} = \text{Speed} \times \text{Time} = (x + 8) \times 5 = 5x + 40
\]

2. Distance traveled on the smaller highway (3 hours):
\[
\text{Distance} = \text{Speed} \times \text{Time} = x \times 3 = 3x
\]

According to the problem, the total distance traveled on both highways is 456 miles:
\[
5x + 40 + 3x = 456
\]

Now, combine the terms:
\[
8x + 40 = 456
\]

Next, subtract 40 from both sides:
\[
8x = 416
\]

Now, divide both sides by 8:
\[
x = 52
\]

Thus, the average speed on the smaller highway is \( \boxed{52} \) miles per hour (option C).