SOLUTION: A fisherman can row a boat 8 km downstream and return in 100 minutes.If the speed of the stream is 2 km per hour.Find the speed of the stream

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Question 696141: A fisherman can row a boat 8 km downstream and return in 100 minutes.If the speed of the stream is 2 km per hour.Find the speed of the stream
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think this should read:
"A fisherman can row a boat 8 km downstream and return in 100 minutes.If the speed of the stream is 2 km per hour.Find the speed of the boat in still water."
Am I right? If so,
Let +s+ = the speed of the boat in still water in km/hr
Let +t+ = the time to go downstream
+s+%2B+2+ = fisherman's speed going down stream in km/hr
+s+-+2+ = fisherman's speed going upstream in km/hr
Convert +100+ min to hours
+100%2F60+=+5%2F3+ hrs
---------------------
Equation going downstream:
(1) +8+=+%28+s+%2B+2+%29%2At+
Equation going upstream:
(2) +8+=+%28+s+-+2+%29%2A%28+5%2F3+-+t+%29+
--------------------------
(1) +t+=+8%2F%28+s+%2B+2+%29+
Substitute (1) into (2)
(2) +8+=+%28+s+-+2+%29%2A%28+5%2F3+-+8%2F%28+s%2B2+%29+%29+
(2) +8+=+%285%2F3%29%2As+-+10%2F3+-+%288s%29+%2F+%28+s%2B2+%29+%2B+16%2F%28+s%2B2+%29+
Multiply both sides by +3%2A%28s+%2B+2%29+
(2) +24%2A%28+s%2B2+%29+=+5s%2A%28+s%2B2+%29+-+10%2A%28+s%2B2+%29+-+24s+%2B+48+
(2) +24s+%2B+48+=+5s%5E2+%2B+10s+-+10s+-+20+-+24s+%2B+48+
(2) +5s%5E2+-+48s+-+20+=+0+
Use quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+-48+
+c+=+-20+
+s+=+%28-%28-48%29+%2B-+sqrt%28+%28-48%29%5E2+-+4%2A5%2A%28-20%29+%29%29+%2F+%282%2A5%29+
+s+=+%28+48+%2B-+sqrt%28+2304+%2B+400+%29%29+%2F+10+
+s+=+%28+48+%2B-+sqrt%28+2704+%29%29+%2F+10+
+s+=+%28+48+%2B+52+%29+%2F+10+ ( can't use the negative square root )
+s+=+100%2F10+
+s+=+10+
The speed of the boat in still water is 10 km/hr
check answer:
(1) +8+=+%28+s+%2B+2+%29%2At+
(1) +8+=+%28+10+%2B+2+%29%2At+
(1) +8+=+12t+
(1) +t+=+2%2F3+
and
(2) +8+=+%28+s+-+2+%29%2A%28+5%2F3+-+t+%29+
(2) +8+=+%28+10+-+2+%29%2A%28+5%2F3+-+t+%29+
(2) +8+=+40%2F3+-+8t+
(2) +8t+=+40%2F3+-+24%2F3+
(2) +8t+=+16%2F3+
(2) +t+=+2%2F3+
OK