SOLUTION: A single-engine plane flies east form an airport at a speed of 140 miles per hour. Two hours later a jet also flies east from the same airport, at a speed of 460 miles per hour. Wr

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Question 540446: A single-engine plane flies east form an airport at a speed of 140 miles per hour. Two hours later a jet also flies east from the same airport, at a speed of 460 miles per hour. Write two systems of equations to help you determine how many minutes it takes the jet to overtake the single-engine plane.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A single-engine plane 140 miles per hour.
Two hours later
a jet speed of 460 miles per hour.
let them meet after x miles
Let plane take t hours
Time taken by plane => x/140=t............(1)
Distance traveled by jet = x miles
speed = 460mph
It tkaes 2 hours less than the plane.
time taken by jet = x/460 = t-2............(2)
Plug t in equation (2)
x/460 = x/140 -2
x/460 - x/140 =-2
(140x-460x)/460*140= -2
-320x= -2*460*140
x= -2*460*140/-320
The distance they meet = 402.5
speed of jet = 460 mph
Time they meet after jet starts =402.5/460
=0.875 hours
=52.5 minutes
CHECK
plane leaves 2 hours early
plane takes 2+0.875 hours
rate of plane = 140 mph
Distance = r *t
2.875*140=402.5 miles
m.ananth@hotmail.ca