Distance rate time

Question

flying against the jet stream, a jet travels 5530 miles in 7 hours. Flying with the jet stream, the same jet travels 5080 miles in 4 hours. what is the rate of the jet in still sir and what is the rate of the jet stream.

Answer 1

velocity = distance/time

Draw a picture and label the positive direction. Define the variables: v_jet is the velocity of the jet and v_wind is the velocity of the wind.

At time 1, velocity = v_jet - v_wind = 5530/7 = 790

At time 2, velocity = -v_jet - v_wind = -5080/4 = -1270

Using elimination to solve by adding the equations we get:

v_jet - v_wind = 790

-v_jet - v_wind = -1270

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-2v_wind = -480

v_wind = 240 miles/hr

Using v_jet - v_wind = 790 and plugging in v_wind = 240 we get:

v_jet - 240 = 790

v_jet = 1030 miles/hr

Answer 2

1.Write a system of equations:

x= speed of jet

y= speed of jet-stream

7(x-y)= 5530 --> x-y= 790

4(x+y)=5080 --> x+y= 1270

2.Solve for x using Elimination Method

x-y=790

x+y=1270

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2x=2060

x=1030

3.Solve for y using Substitution Method

(1030)-y=790

-y=-240

y=240

the speed of the jetstream is 240 mph

the stream of the jet is 1030 mph