You jog at 6.0 mi/h for 5.0 mi, then you jump into a car and drive for another 5.0 mi. With what average speed must you drive if your average speed for the entire 10.0 miles is to be 10.0 mi/h?
To find the average speed, you need to calculate the total distance traveled and the total time taken. The time taken is the sum of the individual times taken for jogging and driving.
First, let's calculate the time taken for jogging. Given that you jog at a speed of 6.0 mi/h for 5.0 mi, you can divide the distance by the speed to get the time:
Time for jogging = Distance / Speed = 5.0 mi / 6.0 mi/h = 0.833 hours
Next, you need to find the time taken for driving. Since the total distance is 10.0 mi (5.0 mi jogging + 5.0 mi driving), you can subtract the distance covered by jogging from the total distance to get the distance covered by driving:
Distance for driving = Total distance - Distance for jogging = 10.0 mi - 5.0 mi = 5.0 mi
To find the average speed for the entire 10.0 miles, you need to divide the total distance by the total time taken:
Average Speed = Total distance / Total time taken
Now, let's solve for the average speed:
10.0 mi/h = 10.0 mi / (0.833 hours + Time for driving)
To isolate the time for driving, we can rearrange the equation:
10.0 mi/h * (0.833 hours + Time for driving) = 10.0 mi
0.833 hours + Time for driving = 10.0 mi / 10.0 mi/h
0.833 hours + Time for driving = 1.0 hour
Subtracting 0.833 hours from both sides:
Time for driving = 1.0 hour - 0.833 hours = 0.167 hours
Now, we know the time taken for driving. To find the average speed for driving, divide the distance covered by driving by the time taken for driving:
Average Speed for driving = Distance for driving / Time for driving = 5.0 mi / 0.167 hours ≈ 29.94 mi/h
Therefore, to have an overall average speed of 10.0 mi/h for the entire 10.0 miles, you must drive at an average speed of approximately 29.94 mi/h.