SOLUTION: Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 4 kilometers an hour faster than the other. If after one hour the

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Question 993681: Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 4 kilometers an hour faster than the other. If after one hour the vehicles are 20 kilometers apart, find the rate of each vehicle.
How would I set up this problem?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the slower vehicle in km/hr
+s+%2B+4+ km/hr = the speed of the faster vehicle in km/hr
+t+=+1+ hr ( given )
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Now find the sides of the right triangle in terms of +s+
Shorter side:
+d%5B1%5D+=+s%2At+
+d%5B1%5D+=+s%2A1+ km
Longer side:
+d%5B2%5D+=+%28+s%2B4+%29%2At+
+d%5B2%5D+=+%28+s%2B4+%29%2A1+ km
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The hypotenuse of the right triangle is given as:
+d+=+20+ km
Use Pythagoerean theorem:
+d%5E2+=+d%5B1%5D%5E2+%2B+d%5B2%5D%5E2+
+20%5E2+=+s%5E2+%2B+%28+s%2B4+%29%5E2+
+400+=+s%5E2+%2B+s%5E2+%2B+8s+%2B+16+
+2s%5E2+%2B+8s+-384+=+0+
+s%5E2+%2B+4s+=+192+
complete the square:
+s%5E2+%2B+4s+%2B+%284%2F2%29%5E2+=+192+%2B+%284%2F2%29%5E2+
+s%5E2+%2B+4s+%2B+4+=+192+%2B+4+
+%28+s%2B+2+%29%5E2+=+14%5E2+
+s+%2B+2+=+14+
+s+=+12+
ans
+s%2B+4+=+16+
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The speed of the slower vehicle is 12 km/hr
The speed of the faster vehicle is 16 km/hr
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check:
+20%5E2+=+s%5E2+%2B+%28+s%2B4+%29%5E2+
+400+=+12%5E2+%2B+16%5E2+
+400+=+144+%2B+256+
+400+=+400+
OK