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 for the entire 10.0 miles, you can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the time it takes for the jogging portion of your trip first. You know that the distance is 5.0 miles and the speed is 6.0 mi/h. So,
Time for jogging = Distance / Speed = 5.0 miles / 6.0 mi/h = 0.83 hours
Next, let's calculate the time it takes for the driving portion. You traveled an additional 5.0 miles and want to find the average speed to make the total average speed 10.0 mi/h. Let's call the average speed for driving as 'x' mi/h.
Time for driving = Distance / Speed = 5.0 miles / x mi/h = 5.0 / x hours
Now, to find the total time for the entire trip, we add the time for jogging and the time for driving:
Total Time = Time for jogging + Time for driving
= 0.83 + 5.0 / x hours
We want the total average speed to be 10.0 mi/h, and we have the formula for average speed:
10.0 mi/h = Total Distance / Total Time
Substituting the known values:
10.0 mi/h = 10.0 miles / (0.83 + 5.0 / x) hours
To solve this equation for 'x', we can rearrange it and solve for 'x':
(10.0 mi/h) * (0.83 + 5.0 / x) = 10.0 miles
(8.3 + 50 / x) = 10.0
50 / x = 10.0 - 8.3
50 / x = 1.7
50 = 1.7x
50 / 1.7 = x
29.41 ≈ x
Therefore, you need to drive at an average speed of approximately 29.41 mi/h to make your overall average speed 10.0 mi/h for the entire 10.0 miles.