#2 

63. AN ILL WIND 

    
It was a fine still day, and the pilots were chatting together on the tarmac at the Adelaide airport.

“Ron and I had a good flight to Sydney and back yesterday,” said pilot Mal. “There was a steady 30-knot wind blowing from the west, but even so, we did the return trip in three hours.”

“I wonder how we will do on this trip,” mused pilot Len. “There is no wind at all today, so we won’t get any help on the flight eastwards.”

“And no hindrance on the way back!” cut in his friend Glen.

“Come on, I don’t reckon the wind makes makes any difference overall. We’ll be back in exactly three hours too!”

Assuming everything else is equal, what do you think?
Hints and strategies

Hint 1

Hint 2

Solution 

Extensions
HINT 1

Think about whether the effect of the wind is dependent on distance travelled or time travelled.
HINT 2

Try setting some numbers or letters for the Adelaide – Sydney distance, the plane speed, and the (effective) wind speed. Now do some calculations for times taken.
SOLUTION

Suppose the distance from Adelaide to Sydney is D and that the plane travels at K km/hr (we ignore the variations at take-off and landing).

With no wind, the total travel time is 2D/K.

Next suppose the wind has an effect on the speed of ± w km/hr.
The time taken is now D/(K – w) + D/(K – w) hours.

We claim (and you can easily check) that this is greater than 2D/K.


Thus in the stated problem, Lan and Glen should be back inside three hours.
EXTENSION

It is easy to construct puzzles of this type which depend on time rather than distance. For example:

If a motor cyclist travels a certain distance at 80 km/hr and back again at 40 km/hr, what is her average speed for the whole trip?

(It’s not what you might think!)