# The problem of the yacht race

In the drawing shown above, two sailboats are in the first part of a race with a triangular path from the buoy TO to B, from this to the C and finally returning to the buoy TO.

The three crew members of the winning sailboat tried to keep track of the speed of the boat but all suffered a severe dizziness and their records were incomplete accordingly.

Smith noted that the sailboat sailed the first three quarters of the race in three and a half hours. Jones warned only that he covered the final three quarters in four and a half hours and Brown was so eager to return to the ground that all he managed to observe was that the intermediate section of the race (of the buoy B to C) took ten minutes longer than the first part.

Assuming that the buoys delimit an equilateral triangle and that the sailboat maintained a constant speed in each section,

Can you tell us how long it took the winning sailboat to finish the race?

#### Solution

The first side of the triangle was traveled in 80 minutes, the second in 90, the last in 160, adding a total time of 5 hours and ½.

We can propose a system of equations that helps us reach the result. We divide the route into 12 parts (remember that it is an equilateral triangle). If we take X as the time spent in the first four parts, X + 10 it will be the corresponding one at four in the middle. Y It represents the time spent for the last four. With this data we can propose the following system of equations with the time expressed in minutes that the solution will give us: