Algebra Problems, Math Problems

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.

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