A jet pilot is making a 1000 mile trip in her military Tomcat. She flies 800 mph for one hour and decides she wants to finish the trip so that she would have flown at an average of 1000 mph. How fast should she go to finish the trip and meet her goal?(Hint: Think carefully about what is meant by average speed").
She must fly faster than the speed of light, that is,
it can't be done.
I want your explanation of why I said that.
Well, I subtracted 1000-800= 200 miles, which was my remaining miles. She wants to finish at an average of 1000 mph so that she would have flown at an average of 1000mph, so speed is 1000mph. I plugged in this values in the formula: average speed=distance/time...
1000=200/time
time=200/1000 and i got 1/5th which is 1/5th of an hour...
no,
it said that she flew at 800 mph for one hour, so she used up 1 hour of flying time
To average 1000 mph in flying 1000 miles would take exactly one hour, which she has already spent flying.
So she must do the remaining 200 miles in zero time.
That is why it is not possible.
To determine the speed at which the pilot should fly in order to achieve an average speed of 1000 mph for the entire trip, we need to consider the concept of average speed. Average speed is the total distance traveled divided by the total time taken.
We know that the pilot has already flown 800 miles in one hour at a speed of 800 mph. To find out the remaining distance she needs to cover, we subtract this distance from the total trip distance: 1000 - 800 = 200 miles.
Let's denote the required speed for the remaining 200 miles as v mph. The time taken to cover this distance will be 200 / v hours.
Now, we need to calculate the total time taken for the entire trip. The first leg took 1 hour, and for the remaining 200 miles, it will take 200 / v hours. So, the total time taken will be 1 + (200 / v) hours.
Considering the formula for average speed (total distance / total time), we can write:
1000 = (800 + 200) / (1 + (200 / v))
Simplifying this equation, we get:
1000 = 1000 (800 + 200) / (v + 200)
We can now solve for v:
v + 200 = (1000 * 1000 * (800 + 200)) / 1000
v + 200 = (800 + 200) * 1000
v + 200 = 1000 * 1000
v = (1000 * 1000) - 200
v ≈ 999,800 mph
Therefore, the pilot should fly at approximately 999,800 mph to meet her goal of having an average speed of 1000 mph for the entire trip.