# Problem of the Day: 2/18/13

Fred can mow a certain lawn in 3 hours. His twin George can mow the same lawn in 2 hours. How long will it take for both of them to mow the lawn together?

Solution to yesterday’s problem:

We notice right away that there is a right triangle whose short leg is 3 inches and whose hypotenuse is 5 inches. Therefore the long leg, PT, is 4 inches. Since PQ is 3 inches as part of the square, the leftover segment QT is 1 inch. Now we notice two similar triangles: the small triangle outside the square and the large triangle, PRT. The ratio of their long legs will be equal to the ratio of their short legs. We can write this as a proportion:

$\frac{4}{1}={3}{x}$

Simplifying,

$4={3}{x}$

$4x=3$

$x=\frac{3}{4}$

We conclude that the length of the lower segment of QS is 3/4 inch.