SOLUTION: Jane traveled 1080 miles by jet and then an additional 180 miles by helicopter. The rate of the jet was four times the rate of the helicopter. The entire trip took a total of 5 hou

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Jane traveled 1080 miles by jet and then an additional 180 miles by helicopter. The rate of the jet was four times the rate of the helicopter. The entire trip took a total of 5 hou      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 760435: Jane traveled 1080 miles by jet and then an additional 180 miles by helicopter. The rate of the jet was four times the rate of the helicopter. The entire trip took a total of 5 hours. Find the rate of the jet.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate of the helicopter be x miles per hour.
Then the rate of jet is +4%2Ax+ miles per hour.
To travel 180 miles by helicopter, time taken would be 180%2Fx hours,
since Time+=+Distance+%2F+Rate
Helicopter time = +180%2Fx .... eqn 1
Similarly, time taken to travel 1080 miles by jet is 1080%2F%284%2Ax%29 hours.
Jet time = 1080%2F%284%2Ax%29 .... eqn 2
It is given that total time, which is the sum of helicopter time + jet time, is 5 hours.
So,
180%2Fx+%2B++1080%2F%284%2Ax%29+=+5 ... eqn 3
Multiplying both sides by 4*x to remove the denominator
180%2A4+%2B+1080+=+5%2A4%2Ax+
or
720+%2B+1080+=+20%2Ax
i.e.
1800+=+20%2Ax Dividing both sides by 20
x+=+1800%2F20+=+90
Rate of helicopter = 90 miles per hour
Therefore, rate of jet = 90%2A4 = 360 miles per hour.
Hope this helps.