# Problem of the Day: 12/20/12

A small plane travels 100 miles in one hour, 600 miles in two hours, then 200 miles in one and a half hours. What is the average speed of the plane throughout the trip?

Solution to yesterday’s problem:
Yay, I get to try out LaTeX!
The original length-to-width ratio is 2:1. So we can designate $x$ as the width and $2x$ as the height. When the length and width are both decreased by 2 inches, the ratio becomes 2.5:1. We’ll change 2.5 to 5/2 and write this equation to represent the change:
$\frac{2x-2}{x-2}=\frac{5}{2}$
Now let’s work this proportion! Cross multiplying,
$2(2x-2)=5(x-2)$
Distributing,
$4x-4=5x-10$
Rearranging by subtracting $4x$ and adding $10$,
$6=x$
So the width of the original board is 6 inches.