Hiking the hill
A certain hill has a lamasery at the bottom and a temple with an altar at the top. The distance along the path is 9 miles from the lamasery to the altar.
When walking up the hill, the lamas walk at a constant speed of 1 mile per hour. When walking down the hill, they walk at a constant speed of 2 miles per hour.
At 9 a.m., a lama departs from the lamasery and heads for the altar. At noon on the same day, a lama leaves the altar and heads for the lamasery.
When they meet, how far in miles are they from the altar?
The answer is 4.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The lama heading uphill has spent 3 hours on the trail by the time the lama heading downhill leaves, and is therefore 6 miles from the altar.
The two lamas then have a closing speed of (2+1) = 3 mph, and it takes (6/3) = 2 hours for them to meet. In 2 hours, the lama heading downhill has hiked 4 miles from the altar.