Question 137397
Hi,

Let the distance covered be = x miles.
Speed of the plane = 300 mph
Speed of wind = 30 mph
So relative speed while going against the wind = 300 - 30 = 270 mph

Thus time taken for covering x miles = distance/rate
                                     = x/270  hrs

 relative speed while retuning alongwith the wind = 300 + 30 = 330 mph
Thus time taken for returning x miles = distance/rate
                                     = x/330  hrs

Given the total time taken = 5 hrs

Thus x/270  + x/330 = 5

==> {{{(11x+9x)/(2970)}}} = 5
[taking 2970 as the common denominator]

==> {{{(20x)/(2970)}}} = 5
==> 20x = 5 * 2970
==> x = 742.5
==> one way the distance = 742.5 miles
So 2 way the distance = 1485 miles.

Thus the plane can safely fly 1485 miles and return with its fuel availability.

Good luck!!!

dolly