SOLUTION: The speed of a stream is 3 km/hr. A boat traveled up stream 4 km in the same time it took to travel 10 km down stream. What was the speed of the boat on still water? I can't fig

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Question 270602: The speed of a stream is 3 km/hr. A boat traveled up stream 4 km in the same time it took to travel 10 km down stream. What was the speed of the boat on still water? I can't figure out how to work this without a time.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = speed of stream in km/hr
Let b = speed of boat in still water in km/hr
Upstream:
d%5B1%5D+=+%28b+-+s%29%2At%5B1%5D
Downstream:
d%5B2%5D+=+%28b+%2B+s%29%2At%5B2%5D
given:
s+=+3 km/hr
d%5B1%5D+=+4 km
d%5B2%5D+=+10 km
t%5B1%5D+=+t%5B2%5D (I'll just call it t)
-------------------------------------------
(1) 4+=+%28b+-+3%29%2At
(1) t+=+4%2F%28b+-+3%29
and
(2) 10+=+%28b+%2B+3%29%2At
(2) t+=+10%2F%28b+%2B+3%29
Since t is the same in both,
4%2F%28b+-+3%29+=+10%2F%28b+%2B+3%29
Multiply both sides by %28b-3%29%2A%28b%2B3%29
4%2A%28b+%2B+3%29+=+10%2A%28b+-+3%29
4b+%2B+12+=+10b+-+30
6b+=+42
b+=+7
The speed of the boat on still water is 7 km/hr
check:
(1) 4+=+%28b+-+3%29%2At
(1) 4+=+%287+-+3%29%2At
(1) 4+=+4t
t+=+1 hr
and
(2) 10+=+%28b+%2B+3%29%2At
(2) 10+=+%287+%2B+3%29%2At
(2) 10+=+10t
t+=+1 hr
OK