Question 75837: "A" and "B" start from the same point and travel along the road that are right angles to each other. "A" travels 3 miles an hour faster than "B". At the end of 2 hours, they are 30 miles apart. Find their rates.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! "A" and "B" start from the same point and travel along the road that are right angles to each other. "A" travels 3 miles an hour faster than "B". At the end of 2 hours, they are 30 miles apart.
:
This will form a right triangle representing the distance traveled by A & B as the
the two legs of the triangle. The hypotenuse is the distance apart they are.
:
Let x = A's speed; then (x-3) = B's speed; time is given as 2 hrs
:
Distance = time * speed:
A's distance = 2x
B's distance = 2(x-3)
:
A's dist^2 + B's dist^2 = 30^2
(2x)^2 + (2(x-3))^2 = 30^2
:
4x^2 + (2x-6)^2 = 900
:
4x^2 + 4x^2 - 24x + 36 = 900
:
8x^2 - 24x + 36 - 900 = 0
:
8x^2 - 24x - 874 = 0
:
Simplify, divide by 8:
x^2 - 3x - 108 = 0
:
Factors to:
(x - 12)(x - 9) = 0
:
x = +12 mph, it's the positive solution we want
:
A's speed = 12 mph
B's speed = 9 mph
:
Check on calc:
Sqrt((2*12)^2 + (2*9)^2) =
Sqrt(24^2 + 18^2) = 30; proves our solutions
:
How about this? Did it make sense to you? Any questions?
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