SOLUTION: sheela can row a boat at the rate of 4km per hour in sill water.she takes 8 hrs in going 12km upstream and 12km downstream.find the speed of the stream.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: sheela can row a boat at the rate of 4km per hour in sill water.she takes 8 hrs in going 12km upstream and 12km downstream.find the speed of the stream.      Log On


   

Question 696791: sheela can row a boat at the rate of 4km per hour in sill water.she takes 8 hrs in going 12km upstream and 12km downstream.find the speed of the stream.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours to go 12 km upstream
+8+-+t+ = time in hours to go 12 km downstream
Let +s+ = the speed of the stream in km/hr
+4+-+s+ = Sheela's speed going upstream in km/hr
+4+%2B+s+ = Sheela's speed going downstream in km/hr
-------------------
Her equation going upstream:
(1) +12+=+%28+4+-+s+%29%2At+
Her equation for going downstream:
(2) +12+=+%28+4+%2B+s+%29%2A%28+8+-+t+%29+
--------------------------
(2) +12+=+32+%2B+8s+-+4t+-+s%2At+
(2) +4t+%2B+s%2At+=+20+%2B+8s+
(2) +t%2A%28+4+%2B+s+%29+=+20+%2B+8s+%29+
(2) +t+=+4%2A%28+5+%2B+2s+%29+%2F+%28+4+%2B+s+%29+
Substitute (2) into (1)
(1) +12+=+%28+4+-+s+%29%2At+
(1) +12+=+%28+4+-+s+%29%2A4%2A%28+5+%2B+2s+%29+%2F+%28+4+%2B+s+%29+
(1) +3%2A%28+4+%2B+s+%29+=+%28+4+-+s+%29%2A%28+5+%2B+2s+%29+
(1) +12+%2B+3s+=+20+-+5s+%2B+8s+-+2s%5E2+
(1) +2s%5E2+=+20+-+12+
(1) +2s%5E2+=+8+
(1) +s%5E2+=+4+
(1) +s+=+2+
The speed of the stream is 2 km/hr
check answer:
(1) +12+=+%28+4+-+2+%29%2At+
(1) +12+=+2t+
(1) +t+=+6+
and
(2) +12+=+%28+4+%2B+2+%29%2A%28+8+-+t+%29+
(2) +12+=+6%2A%28+8+-+t+%29+
(2) +8+-+t+=+2+
(2) +t+=+8+-+2+
(2) +t+=+6+
OK