E-Newsletter Brain Teaser December 2009

Ann went from Point A to Point B.

Simultaneously Peter went from B to A.
In six hours they met and in another three hours Peter reached A.
How many hours did Ann travel from A to B?

Peter’s total travel time was 9 hours.
Assume both travel at a constant speed:
Let’s pick a speed for Peter…60 miles per hour so Peter will travel 540 miles altogether (as will Ann). He travelled 360 miles in the first 6 hours and 180 miles in the last 3 hours for a total of 540 miles.

after 6 hours, they were both much closer to A than to B


A----------------X---------------------------------B

If Ann took 6 hours to travel her 180 miles (540-360), she was only travelling 30 mph.
So it will take Ann 18 hours to travel from A to B. (540/30)

If we pick another speed, let’s say 100 mph for Peter
So he travelled 600 miles in the first 6 hours and 300 miles in the last 3 hours for a total of 900 miles.

If Ann took 6 hours to travel her 300 miles, therefore she was only travelling 50 mph.
So it will take Ann 18 hours to travel from A to B. (900/18)

Many apologies for a typo, the original problem in the e-newsletter said:
In six hours they met and in another three hours Peter reached B.