Flying against the jetstream, a jet travels 2700 miles in 5 hours. Flying with the jetstream, the same jet travels 8820 miles in 9 hours. What is the rate of the jet in still air and what is the rate of the jetstream?
Question
Flying against the jetstream, a jet travels 2700 miles in 5 hours. Flying with the jetstream, the same jet travels 8820 miles in 9 hours. What is the rate of the jet in still air and what is the rate of the jetstream?
Solution
Let's denote the rate of the jet in still air as J and the rate of the jetstream as S.
When the jet is flying against the jetstream, the effective speed of the jet is (J - S) because the jetstream is slowing it down. So, we can write the equation for the distance covered as:
2700 = 5(J - S) ...(equation 1)
When the jet is flying with the jetstream, the effective speed of the jet is (J + S) because the jetstream is helping it along. So, we can write the equation for the distance covered as:
8820 = 9(J + S) ...(equation 2)
Now we have a system of two equations, and we can solve it step by step.
First, let's simplify both equations:
From equation 1: 2700 = 5J - 5S => 540 = J - S From equation 2: 8820 = 9J + 9S => 980 = J + S
Now we have a new system of equations:
540 = J - S ...(equation 3) 980 = J + S ...(equation 4)
We can solve this system by adding these two equations together:
540 + 980 = J - S + J + S 1520 = 2J J = 1520 / 2 J = 760 mph
Substitute J = 760 mph into equation 4:
980 = 760 + S S = 980 - 760 S = 220 mph
So, the rate of the jet in still air is 760 mph and the rate of the jetstream is 220 mph.
Similar Questions
A jet travels 3170 miles against the wind in 5 hours and 4170 miles with the wind in the same amount of time. What is the rate of the jet in still air and what is the rate of the wind?
A boat can go 18 miles downstream in the same time it takes to go 12miles upstream. The rate of the water is 6 mph. What is the rate of the boat?
A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in 8 hours. Find the speed of the boat in still water and the speed of the stream respectively.
A boat travels downstream from A to B, halts for 5 minutes at B, then travels upstream to C. The entire trip takes 4 hrs. Had the boat travelled the entire distance in still water, the boat would have taken 4 hrs. If the speed of the boat in still water and the speed of the stream are 10 km/hr and 2 km/hr respectively, find BC (in km).
A man rows to a place 35 km in distance and back in 10 hours 30 minutes. He found that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of flow of the stream?Options1.5 km/hr0.75 km/hr1 km/hr1.33 km/hr
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.