SOLUTION: At 8:00 am Nancy took off down a river in her boat heading north. Two hours later, William takes off down the same river in his boat also heading north. Nancy's boat speed is 3km/h

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Question 1021016: At 8:00 am Nancy took off down a river in her boat heading north. Two hours later, William takes off down the same river in his boat also heading north. Nancy's boat speed is 3km/hour more than William's. At 12:00 pm, Nancy is 44 km ahead of William. What is the speed of each boat?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Nancy's boat speed
+s+-+3+ = William's boat speed
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Nancy's head start is:
+d%5B1%5D+=+s%2A2+
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Time the boats from 10 PM to 12 PM
Let +d+ = distance in km from Nancy's
starting point at 10 PM
Nancy's equation:
(1) +d+=+s%2A2+
William's equation:
+d+%2B+d%5B1%5D+-+44+=+%28+s+-+3+%29%2A2+
(2) +d+%2B+2s+-+44+=+%28+s+-+3+%29%2A2+
--------------------------
Substitute (1) into (2)
(2) +2s+%2B+2s+-+44+=+%28+s+-+3+%29%2A2+
(2) +4s+-+44+=+2s+-+6+
(2) +4s+-+2s+=+38+
(2) +2s+=+38+
(2) +s+=+19+
and
+s+-+3+=+16+
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Nancy's speed is 19 km/hr
William's speed is 16 km/hr
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check:
(1) +d+=+s%2A2+
(1) +d+=+2%2A19+
(1) +d+=+38+
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From 8PM to 10 PM, Nancy goes
+19%2A2+=+38+ km
From 10 PM to 12 PM, Nancy goes
+19%2A2+=+38+ km
-----------------
In the 4 hrs, she has gone +2%2A38+=+76+ km
From 10 PM to 12 PM, William goes
+16%2A2+=+32+ km
+76+-+32+=+44+ km
He is +44+ km behind her
Hope I got it!