Answer:
Explanation:
Suppose the distance between the two cities is D and the velocity in calm weather is V . The total time taken in two way travel is given by
Total distance / velocity
= 2 D / V
Suppose velocity of wind is v . Then in one way the velocity of airplane will become V + v and in the return trip its velocity will be V - v
Total time taken
= [tex]\frac{D}{V+v} +\frac{D}{V-v}[/tex]
= [tex]\frac{2DV}{V^2-v^2}[/tex]
= [tex]\frac{2V^2D}{V(V^2-v^2)}[/tex]
= [tex]\frac{2D}{V(1 - \frac{v^2}{V^2}) }[/tex]
= The denominator contains a factor
[tex]1-\frac{v^2}{V^2}[/tex]
which is less than one so time calculated will be more than
2D / V
Hence in the second case time taken will be more .
