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

10 mph
10 mph

50 mph
50 mph

60 mph .

Answer 1

To find the average speed for each route, you can use the formula:

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

For the first route:
- Distance = 400 miles
- Time = 8 hours

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

For the second route:
- Distance = 420 miles
- Time = 7 hours

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

Now, to find how much higher the average speed is on the faster route, subtract the average speed of the first route from the average speed of the second route:

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

Therefore, the average speed on the faster route is 10 mph higher.

**Final Answer:** 10 mph