An airplane flew a distance of 1500 Km against a wind speed of 100
km/hr. On the return flight the airplane flew with the wind of same
speed and took 1 hour and 15 minutes less. Find the speed of the
airplane, assuming the speed remained the same during both the trips.
The value required as answer is generally assumed as a variable in word problems.
So, let the speed of the airplane = x Km/hr.
Let us form a distance, speed, time table for the situation required.
Direction of the wind 
Distance

Speed of the Flight 
Time taken for the flight 
With wind 
1500 Km 
x + 100 
$\frac{1500}{x+100}$ 
Against wind  1500 Km  x  100  $\frac{1500}{x100}$ 
The equation is formed, using the difference in the times.
$\frac{1500}{x100}$ 
$\frac{1500}{x+100}$ =
$1\frac{1}{4}$ (The time difference is written in hours)
$4(x  100)(x + 100)$ . (
$\frac{1500}{x100}$ 
$\frac{1500}{x+100}$) =
$\frac{5}{4}$ $\times$ $4(x  100)(x + 100)$ (Multiplied by LCD)
6000(x + 100)  6000(x 100) = 5x
^{2}  50000 (Distributive Property)
6000x + 600000  6000x + 600000 = 5x
^{2}  50000
5x
^{2} = 1250000 (Equation simplified)
x
^{2} = 250000 ⇒ x = 500
Hence the speed of the airplane =
500 Km/hr