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