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# Runners A and B leave the same point P at right angles. A runs 4 m/h faster than B. After 2 hours they are 40 km apart. Find the speed of A

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Runners A and B leave the same point P at right angles. A runs 4 m/h faster than B. After 2 hours they are 40 km apart. Find the speed of A and B. ( let x = to the speed of A)

Feb 24, 2015

### Best Answer

#1
+94558
+5

Let B's rate = x  ...then A's rate = x + 4

The distance that A runs is ..... time x rate = 2(x + 4)

The distance that B runs is..... time x rate = 2x

And using the Pytagorean Theorem, we have

(2x)^2 + [2(x + 4)]^2  = 40^2

4x^2 + 4(x^2 + 8x + 16)  = 1600

4x^2 + 4x^2 + 32x + 64 = 1600

8x^2 + 32x - 1536  = 0  divide through by 8

x^2 + 4x - 192  = 0     factor

(x +16) ( x - 12) = 0

And setting each factor to 0, we have that x = -16 and x = 12

Reject the -16

So ... A's speed = x + 4 = 12 + 4 = 16 km/hr

Feb 24, 2015

### 1+0 Answers

#1
+94558
+5
Best Answer

Let B's rate = x  ...then A's rate = x + 4

The distance that A runs is ..... time x rate = 2(x + 4)

The distance that B runs is..... time x rate = 2x

And using the Pytagorean Theorem, we have

(2x)^2 + [2(x + 4)]^2  = 40^2

4x^2 + 4(x^2 + 8x + 16)  = 1600

4x^2 + 4x^2 + 32x + 64 = 1600

8x^2 + 32x - 1536  = 0  divide through by 8

x^2 + 4x - 192  = 0     factor

(x +16) ( x - 12) = 0

And setting each factor to 0, we have that x = -16 and x = 12

Reject the -16

So ... A's speed = x + 4 = 12 + 4 = 16 km/hr

CPhill Feb 24, 2015

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