Synchronize two clocks

Problem:
There is a clock at the bottom of the hill and a clock at the top of the hill. The clock at the bottom of the hill works fine but the clock at the top doesn’t. How will you synchronize the two clocks. Obviously, you can’t carry either of the clocks up or down the hill! And you have a horse to help you transport yourself. And, the time required for going up the hill is not equal to the time required to go down the hill.

Solution:
Let h1 be the time required to climb up to the top of the mountain on the horseback and h2 be the time required to climb down to the bottom on the horseback.

Let p1 and p2 be times required for the person to climb up and climb down on foot.

The person has to make four different kinds of round-trips and measure the round trip times.

1. Climb up and climb down on horseback. The round trip time would be: h1 + h2 = t1 (t1 is measured accurately using the clock at the bottom)
2. Climb up and climb down on foot. The round trip time would be: p1 + p2 = t2
3. Climb up on horseback and climb down on foot. The round trip time would be: h1 + p2 = t3
4. Climb up on foot and climb down on horseback. The round trip time would be: p1 + h2 = t4

Now we have four equations and four unknowns:
h1 + h2 = t1
p1 + p2 = t2
h1 + p2 = t3
p1 + h2 = t4

(t1 to t4 are measured values and hence are known). Solving the system of linear equations gives the values of h1, h2, p1 & p2.

Now start from the bottom of the hill, record the time, call it t, using the clock at the bottom and climb up either on horseback or on foot.

Once you reach the top, correct the clock's time at the top to be either t + h1(if you have climbed up the hill on horseback) or t + p1(if you have climbed up the hill on foot).

Links and credits:
http://www.careercup.com/question?id=20676667