Question

A piece of land is shaped like a right triangle. Two people start at the right angle vertex of the triangle at the same time and walk the same speed along different legs of the triangle. If the area formed by the positions of the two ppl and their starting point (the right angle) is changing at 4m²/sec, then how fast are the ppl moving when they are 5m from the right angle?

Answer 1

Think of this as a difference in areas problem: subtract one right triangle having two legs of 5m from another having two legs each 5m+dx, where dx is the rate at which the two individuals are travelling. This difference is equal to 4m^2/s:

((5+dx)^2)/2-(5^2)/2=4m^2/s

(25+10*dx+dx^2-25)/2=4

(dx^2+10*dx)/2=4

dx^2+10*dx-8=0

Use the quadratic equation to solve for dx. Choose the positive answer.