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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(22740)   (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
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