Sheela can row a boat at the rate of 4 kilometre per hour in stillwater. She takes 8 hours in going twice the numerator upstream and 12 kilometre downstream find the speed of stream.
Answers
Step-by-step explanation:
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