August 2019

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?

Solution:
Let Rate of pedro = 1/tpedro = x
Rate of juan = .50x
Rate of pilar = .80x
(x+.50x+.80x)4=1
2.3x=1/4
x=5/46
5/46 = 1/tpedro
tpedro=46/5 =9.2hours

From the figures shown below. Squares EGHI and KHJB are fixed. Show that the area of triangle ABH is constant regardless of the dimensions of square ADEF.
 

Figure 1

Figure 2

Good day sir!
"A frustum of a regular pyramid has a lower base of 12cm by 12cm and an upper base of 8cm by 8cm. If the lateral edge is 18cm, compute the volume of the regular pyramid."

The answer is V=1801.71cm3 which is actually the volume of the frustum. Is he correct sir? Because i was thinking i should get the whole volume of the square based regular pyramid.

If a^x = b, b^y = c, and c^x = a, prove that the product xyz = 1.