To solve this problem, we can calculate the average speed for both routes using the formula:
\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \]
Route 1:
- Distance: 400 miles
- Time: 8 hours
Using the formula: \[ \text{Average Speed for Route 1} = \frac{400 \text{ miles}}{8 \text{ hours}} = 50 \text{ miles per hour} \]
Route 2:
- Distance: 20 miles
- Time: 7 hours
Using the formula: \[ \text{Average Speed for Route 2} = \frac{20 \text{ miles}}{7 \text{ hours}} \approx 2.857 \text{ miles per hour} \]
Difference in Average Speeds:
Now, to find out how much higher the average speed is on the faster route (Route 1) compared to Route 2, we can subtract the average speed of Route 2 from Route 1.
\[ \text{Difference} = \text{Average Speed for Route 1} - \text{Average Speed for Route 2} \] \[ \text{Difference} = 50 \text{ miles per hour} - 2.857 \text{ miles per hour} \approx 47.143 \text{ miles per hour} \]
Summary:
- Average Speed for Route 1: 50 miles per hour
- Average Speed for Route 2: approximately 2.857 miles per hour
- The average speed on the faster route (Route 1) is approximately 47.143 miles per hour higher than the speed on Route 2.
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