Question

Suppose a Southwest Airlines passenger plane took three hours to fly 1800 miles in the direction of the Jetstream. The return trip against the Jetstream took four hours. What was the plane’s speed (as read on the plane’s speedometer) in still air and the Jetstream’s speed? How can applying matrices and linear systems help solve this problem?

Answer 1

plane speed: 525mph, jetstream speed=75mph, in explanation it is solved with a linear equations system

Step-by-step explanation:

First lets name each speed

vs:=speed of the jetstream

vp:=speed of the plane

Now when in the jetstream direction the speeds are added and on the opposite direction are subtracted, then we get these equations, that are linear.

1800 mi=(vp+vs)*3h

1800 mi=(vp-vs)*4h

which is a linear equation system equivalent to:

600 mph=vp+vs (1)

450 mph=vp-vs (2)

Now from (2) vp= 450mph+vs (3), replacing this in (1) we get:

600mph=(450mph+vs)+vs=450mph+2*vs, then 2*vs=150mph or vs=*75mph, this is the jetstream speed, replacing this in (3) we get the plane speed too vp=450 mph +75mph = 525 mph