### CAT 2007 Question 6

Instructions

Directions for the following two questions: Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non-stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west. It reduces or increases the speed of plane by 50 km per hour depending on direction of flight.

Question 6

# What is the plane’s cruising speed in km per hour?

Solution

Let the speed of the plane be p Kmph.

So the speed of plane from A to B will be 'p+50' and the speed from B to A will be 'p-50'.

We notice that the plane goes from B to A stays there for 1 hr and again come back to B with total time duration 12 hrs.

So we have $$\frac{3000}{p-50} + 1 + \frac{3000}{p+50} = 12$$.

On substituting the options, we can clearly see that speed of the plane is 550 which satisfies the above equation.