Flying against the wind, a jet travels 3220 miles in 7 hours. Flying with the wind, the same jet travels 2820 miles in 3 hours. What is the rate of the jet in still air and what is the rate of the wind?
Since speed * time = distance, we have (with jet=j and wind=w):
7(j-w) = 3220
3(j+w) = 2820
j=700
w=240
To find the rate of the jet in still air, we can use the formula:
Rate of the jet in still air = (Rate of the jet with the wind + Rate of the jet against the wind) / 2
Similarly, to find the rate of the wind, we can use the formula:
Rate of the wind = (Rate of the jet with the wind - Rate of the jet against the wind) / 2
Let's start by finding the rate of the jet with the wind. We know that when the jet is flying with the wind, it travels 2820 miles in 3 hours. Therefore, the rate of the jet with the wind is calculated by dividing the distance by the time:
Rate of the jet with the wind = 2820 miles / 3 hours = 940 miles per hour (mph).
Next, let's find the rate of the jet against the wind. We know that when the jet is flying against the wind, it travels 3220 miles in 7 hours. Therefore, the rate of the jet against the wind is calculated by dividing the distance by the time:
Rate of the jet against the wind = 3220 miles / 7 hours = 460 miles per hour (mph).
Now, let's substitute the values we found into the formulas to calculate the rate of the jet in still air and the rate of the wind:
Rate of the jet in still air = (940 mph + 460 mph) / 2 = 1400 mph
Rate of the wind = (940 mph - 460 mph) / 2 = 240 mph
So, the rate of the jet in still air is 1400 mph, and the rate of the wind is 240 mph.