To find the average speed for each route, we can use the formula:
\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} \]
- For the first route (400 miles in 8 hours):
\[ \text{Average speed}_{1} = \frac{400 \text{ miles}}{8 \text{ hours}} = 50 \text{ mph} \]
- For the second route (420 miles in 7 hours):
\[ \text{Average speed}_{2} = \frac{420 \text{ miles}}{7 \text{ hours}} = 60 \text{ mph} \]
Now, to find out how much higher the average speed is on the faster 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.
The answer is 10 mph.