Problema Solution
A passenger plane and a jet leave at the same time from the same airport, traveling in opposite directions. The jet travels at twice the speed of the plane. They are 2400 miles apart in 4 hours. Find the rates of both the plane and the jet.
Answer provided by our tutors
let
j = the rate (avg. speed) of the jet plane
p = the rate of the passenger plane
t = 4 h the time of the travel
d = 2400 miles the distance between the planes
the jet travels at twice the speed of the plane
j = 2p
they are 2400 miles apart in 4 hours
since avg.speed=distance/time => distance = avg.speed*time
the distance that the jet will travel = j*t = 4j miles
the distance that the plane will travel = p*t = 4p miles
the distance between them is 2400 miles thus
4j + 4p = 2400 divide both sides by 4
j + p = 2400/4
j + p = 600
by solving the system of equations
j = 2p
j + p = 600
we find
j = 400 mph
p = 200 mph
click here to see the step by step solution of the system of equations
the rate of the jet is 400 mph.
the rate of the plane is 200 mph.