Briefly

From Villarriba to Villabajo

From Villarriba to Villabajo

To go from Villarriba to Villabajo I use a car that, when traveling down a mountain, runs at 72 km / h, on flat land at 63 km / h and uphill at 56 km / h.

If it takes 4 hours to go from Villarriba to Villabajo, to return to work 4 hours and 40 minutes and we know that there is a flat part of the route,

How far is Villarriba from Villabajo?

Solution

If we call to to the climb section, b to the flat section and c to the section of descent, from the statement, we obtain the following equations:

a / 72 + b / 63 + c / 56 = 4 hours
a / 56 + b / 63 + c / 72 = 14/3 hours

If we multiply both equations by 7 * 8 * 9 we will have:

7 * a + 8 * b + 9 * c = 4 * 7 * 8 * 9 hours
9 * a + 8 * b + 7 * c = (14/3) * 7 * 8 * 9 hours

And if we add both we have:
16 * (a + b + c) = 7 * 8 * 9 * (12 + 14) / 3

Where do we get that a + b + c = 7 * 3 * 13 = 273 Km