Question 760435
Let the rate of the helicopter be {{{x}}} miles per hour.

Then the rate of jet is {{{ 4*x }}} miles per hour.

To travel 180 miles by helicopter, time taken would be {{{180/x}}} hours,

since {{{Time = Distance / Rate}}}

Helicopter time = {{{ 180/x}}} .... eqn 1

Similarly, time taken to travel 1080 miles by jet is {{{1080/(4*x)}}} hours.

Jet time = {{{1080/(4*x)}}} .... eqn 2

It is given that total time, which is the sum of helicopter time + jet time, is 5 hours.

So, 

{{{180/x +  1080/(4*x) = 5}}} ... eqn 3

Multiplying both sides by 4*x to remove the denominator

{{{180*4 + 1080 = 5*4*x }}}

or

{{{720 + 1080 = 20*x}}}

i.e.

{{{1800 = 20*x}}} Dividing both sides by 20

{{{x = 1800/20 = 90}}}

Rate of helicopter = 90 miles per hour
Therefore, rate of jet = {{{90*4}}} = {{{360}}} miles per hour.

Hope this helps.