Related rates porblem Please help.

[dungas]

I'm in grade 12 and this was given on a test and I had no clue how to solve it (it was a bonus question)

If two men are running away from each other at 45 degrees and man1 is running at 12 km/h and man2 is running at 10 km/h; How fast are they moving apart at 2.5 hours?


So I first made a drawing:
Is that correct?

I have no clue how to come up with an equation with respect to time.

Please help

[nona.m.nona]

I would suggest labelling the two sides as "x" and "y", so their speeds are "dx/dt" and "dy/dt", respectively. The distance D is the vertical side's length. Then note that this is a right triangle, so x² + D² = y² (assuming "y" is the hypotenuse). Differentiate, etc.