Find the rate of the jet

Question

Jane travelled 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 1

Let

v = the rate of the holicopter. So 4v = the rate of the jet.

Balance by the total time,

1080/(4v) + 180/v = 5

Multiply both sides by 4v,

1080+720 = 20v

v = 90 mph

4v = 360 mph

Answer: The rate of the jet is 360 mph.

 

Answer 2

Hi Donald;

[(1080 miles)/(4H miles/hour)]+[(180 miles)/(H miles/hour)]=5 hours

Let's note that the unit //hour in the denominator, is the unit hour in the numerator...

[(1080 miles)/(4H miles)]+[(180 miles)/(H miles)]hours=5 hours

Let's note the unit of miles in the numerator and denominator of each bracketed equation.  These cancel...

[(1080 miles)/(4H miles)]+[(180 miles)/(H miles)]hours=5 hours

[(1080/4H)+(180/H)]hours=5 hours

Let's note that the unit of hours in the numerator of both sides of the equation cancels...

[(1080/4H)+(180/H)]hours=5 hours

(1080/4H)+(180/H)=5

Let's multiply (180/H) by (4/4)...

(1080/4H)+(720/4H)=5

1800/4H=5

Let's cross-multiply...

1800=20H

90=H

360=4H=Jet

The helicopter traveled at 90 miles/hour.

The jet traveled at 360 miles/hour.

 

 

Answer 3

Hey Donald -- here's a "verbal" approach with easy 'test values' ... 7 'legs' of 180mi ...

 

if chopper takes 1hr, then jet moves 720mph taking way less than 4hrs ...

 

if chopper takes 2hr, then jet moves 360mph taking 3hrs ==> jet 360mph ... Regards :)