You jog at 6.6 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 10.4 mi/h?
answer is 24.5 mi/h.
WHY??
let the speed in the car be x mph
so 5/6.6 + 5/x = 10/10.4
5/x = 10/10.4 - 5/6.6
5/x = .20396
x = 5/.20396
x = 24.5
he should drive the last 5 miles at 24.5 mph
check
if avg speed is 10.4 mph, then it took
10/10.4 hours or .9615 hours
time jogging = 5/6.6 = .7576 hours
time in car = 5/24.5 = .20408 hours
for a total time of .96166 hours
allowing for roundoff errors, close enough!
To find the average speed for the entire 10.0 miles, you need to consider the time it takes to cover each distance at different speeds.
Let's start by calculating the time it takes to jog for 5.0 miles. Since you jog at 6.6 mi/h, you can use the formula:
Time = Distance / Speed
The time it takes to jog 5.0 miles is:
Time = 5.0 miles / 6.6 mi/h = 0.758 hours
Next, let's calculate the time it takes to drive for another 5.0 miles at an unknown average speed. We will denote this speed as 'v'. The formula for time in this case would be:
Time = Distance / Speed
The time it takes to drive 5.0 miles at an average speed of 'v' mi/h is:
Time = 5.0 miles / v mi/h = 5/v hours
The total time for the entire 10.0 miles must be equal to (10.0 miles / 10.4 mi/h) to maintain an average speed of 10.4 mi/h. Therefore, the total time would be:
Total Time = 10.0 miles / 10.4 mi/h = 0.962 hours
Now, we can set up an equation based on the sum of the individual times. The total time for the jog plus the total time for the drive must be equal to the desired total time of 0.962 hours, so:
0.758 hours + (5.0 miles / v mi/h) = 0.962 hours
To find 'v', we need to solve this equation. First, subtract 0.758 hours from both sides:
(5.0 miles / v mi/h) = 0.962 hours - 0.758 hours
(5.0 miles / v mi/h) = 0.204 hours
Next, multiply both sides by 'v' to isolate the variable:
5.0 miles = 0.204 hours x v mi/h
5.0 miles = 0.204v mi
To solve for 'v', divide both sides by 0.204:
v mi = 5.0 miles / 0.204
v mi ≈ 24.51 mi/h
Therefore, to achieve an average speed of 10.4 mi/h for the entire 10.0 miles, you would need to drive at an average speed of approximately 24.51 mi/h. This is why the answer is 24.5 mi/h (rounded to the nearest tenth).
To find the average speed for the entire 10.0 miles, we need to consider the time taken for both jogging and driving.
Let's first calculate the time taken for jogging using the formula: time = distance / speed.
Time taken for jogging = 5.0 miles / 6.6 mi/h
= 0.7576 hours
Next, we need to calculate the time taken for driving. To do this, we can use the formula: time = distance / speed. Since we're trying to find the average speed for the entire 10.0 miles, we'll assume that the remaining 5.0 miles were covered entirely by driving.
Time taken for driving = 5.0 miles / speed
Now, the total time taken for the entire 10.0 miles can be found by adding the time taken for jogging and driving.
Total time = time taken for jogging + time taken for driving
= 0.7576 hours + (5.0 miles / speed)
We're given that the average speed for the entire 10.0 miles is 10.4 mi/h, so we can set up the equation:
10.4 mi/h = total distance / total time
= 10.0 miles / (0.7576 hours + (5.0 miles / speed))
Now, we can solve for the average speed by cross-multiplying and simplifying the equation:
10.4 mi/h * (0.7576 hours + (5.0 miles / speed)) = 10.0 miles
10.4 mi/h * 0.7576 hours + (10.4 mi/h * 5.0 miles / speed) = 10.0 miles
7.92 + (52 miles/speed) = 10.0 miles
52 miles/speed = 2.08
speed = 52 miles / 2.08
speed ≈ 24.5 mi/h
Therefore, to achieve an average speed of 10.4 mi/h for the entire 10.0 miles, you must drive at an average speed of approximately 24.5 mi/h.