I was taking this aptitude question, and I had this confusing math problem in it I couldn't figure out.
An airplane is travelling 2400 miles from A to B. It is going at 600 mph with a tailwind of 40 mph. After what point in time should it have taken longer to go back to point A than to complete the route to point B?
My original answer was 2 hours, which turned out to be wrong. Anyone else knows how to solve this.
Assume the plane is going 600 mph and that includes the tailwind. That means its speed is $600-40=560$ mph. So when it turns around, the the tailwind becomes a headwind and its speed becomes $560-40=520$. As it takes longer to make the return trip, the turnaround time would be before 2 hours (the halfway point).
Let $d$ be the distance traveled and $v$ the speed of the plane. You can find time $t$ when $t=\frac{d}{v}$. For the trip to point $B$, $t=\frac{2400-d}{600}$. For the trip back to point $A$, $t=\frac{d}{520}$. The answer you seek is when the two quantities are equal. In other words, solve for $d$.
Now assume the plane's speed is 600 mph plus the tailwind, for a total speed of 640. The speed on the return journey is then 560 mph. Use these values in your equation and solve for $d$. If it's a multiple choice test, only one of the answers should be among the choices.