Question

You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?(1 point)
Responses

20 mph
20 mph

60 mph
60 mph

10 mph
10 mph

50 mph

Answer 1

To find the average speed for each route, we can use the formula for speed, which is:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

**For Route 1:**

- Distance = 400 miles
- Time = 8 hours

Calculating the average speed:

\[
\text{Speed}_1 = \frac{400 \text{ miles}}{8 \text{ hours}} = 50 \text{ mph}
\]

**For Route 2:**

- Distance = 420 miles
- Time = 7 hours

Calculating the average speed:

\[
\text{Speed}_2 = \frac{420 \text{ miles}}{7 \text{ hours}} = 60 \text{ mph}
\]

Now, to find how much higher the average speed is on the faster route (Route 2) compared to Route 1:

\[
\text{Difference in speed} = \text{Speed}_2 - \text{Speed}_1 = 60 \text{ mph} - 50 \text{ mph} = 10 \text{ mph}
\]

Thus, the average speed of Route 2 is 10 mph higher than that of Route 1.

The answer is **10 mph**.