# SOLUTION: Runners Aaron and Ben leave the same oint P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each.

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Runners Aaron and Ben leave the same oint P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each.      Log On

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 Question 375989: Runners Aaron and Ben leave the same oint P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each.Answer by ankor@dixie-net.com(15656)   (Show Source): You can put this solution on YOUR website!Runners Aaron and Ben leave the same point P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each. : We will use a^2 + b^2 = c^2, to solve this problem Let a = Aaron's running speed In two hrs, he will have run 2a km then (a-4) = Ben's running speed In two hrs, he will have run (2a-8)km : c = 40 : (2a)^2 + (2a-8)^2 = 40^2 4a^2 + 4a^2 - 32a + 64 = 1600 8a^2 - 32a + 64 - 1600 = 0 8a^2 - 32a - 1536 = 0; our old friend, the quadratic equation! Simplify, divide by 8 a^2 - 4a - 192 = 0 Factor this to (a-16)(a+12) = 0 positive solution a = 16 km/hr is Aaron's speed and 12 km/hr is Ben's speed ; : Check this out 32^2 + 24^2 = 40^2 1024 + 576 = 1600