System of equations

Question

A plane flew 2,100km with the jet stream in 2.5hrs the return flight against the jet stream took 3.75hrs. Find the speed of the jet stream and the airspeed of the plane using the system of equations method

Answer 1

Let S be the airspeed of the plane.

Let J be the speed of the jetstream.

 

When the plane is flying with the jetstream, its effective speed is increased by the speed of the jetstream, so it is equal to S+J

 

When the plane is flying against the jetstream, its effective speed is decreased by the speed of the jetstream, so it is equal to S-J

 

The distance = speed * time

 

In each case the distance is 2100

 

When the plane is flying wiht the jetstream, it took 2.5 hours to go 2100 km

Then (S+J)*2.5 = 2100

Or S+J = 2100/2.5 = 840

 

When the plane is flying against the jetstream it took 3.75 hours to go 2100 km

Then (S-J)*3.75 = 2100

S-J = 2100/3.75 = 560

 

So the two equations are

S+J=840

S-J=560

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Add the two equations together:

 

S+J+S-J = 840 + 560

2*S = 1400

S = 700 km/h

 

Since S+J = 840

700+J=840

J= 840 - 700 = 140 km/h

 

Airspeed of plane is 700km/h

speed of jetstream is 140 km/h