SOLUTION: A boat travels 15km/hr in still water. In travelling 45 km downstream from Town A to Town B, it completes the journey in 75 minutes less than it takes for the return journey. At wh

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Question 851788: A boat travels 15km/hr in still water. In travelling 45 km downstream from Town A to Town B, it completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?
Please explain simply. Apparently I am an idiot.
Found 2 solutions by lwsshak3, josmiceli:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A boat travels 15km/hr in still water. In travelling 45 km downstream from Town A to Town B, it completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?
***
let x=speed of river flow
15+x=speed of boat downstream
15-x=speed of boat upstream
travel time=distance/speed
...
travel time upstream=45/(15-x) (return trip)
travel time downstream=45/(15+x)
75 min=(75/60) hr
45%2F%2815-x%29-45%2F%2815%2Bx%29=75%2F60
LCD:(15-x)(15+x)(60)
60%2A45%2815%2Bx%29-60%2A45%2815-x%29=75%2815-x%29%2815%2Bx%29
40500+2700x-40500+2700x=75(225-x^2)
5400x=16875-75x^2
75x^2+5400x-16875=0
divide by 75
x^2+72-225=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=72, c=-225
ans:
x=-12.37 (reject)
or
x=12.37
speed of river flow=12.37 km/hr

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's not easy and probably not a
test of intelligence
Let +c+ = the speed of the river ( c for current )
+15+%2B+c+ = the speed of the boat going downstream
+15+-+c+ = the speed of the boat going upstream
Let +t+ = the time in hours to travel
from A to B going downstream
+t+%2B+75%2F60+ = the time in hours to travel
from B to A going upstream
-----------------------------------------
Equation for going downstream:
(1) ++45+=+%28+15+%2B+c+%29%2At+
Equation for going upstream:
(2) +45+=+%28+15+-+c+%29%2A%28+t+%2B+75%2F60+%29+
---------------------------------
(2) +45+=+%28+15+-+c+%29%2A%28+t+%2B+5%2F4+%29+
(2) +45+=+15t+-+c%2At+%2B+75%2F4+-+%285%2F4%29%2Ac+
(2) +45+=+t%2A%28+15+-+c+%29+%2B+75%2F4+-+%285%2F4%29%2Ac+
and
(1) +t+=+45+%2F+%28+15+%2B+c+%29+
substitute this into (2)
(2) +45+=+%28+45+%2F+%28+15+%2B+c+%29+%29%2A%28+15+-+c+%29+%2B+75%2F4+-+%285%2F4%29%2Ac+
Multiply both sides by +4%2A%28+15+%2B+c+%29+
(2)
(2) +2700+%2B+180c+=+2700+-+180c+%2B+1125+%2B+75c+-+75c+-+5c%5E2+
(2) +360c+=+1125+-+5c%5E2+
(2) +5c%5E2+%2B+360c+-1125+=+0+
(2) +c%5E2+%2B+72c+-+225+=+0+
Use quadratic formula
+C+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ( C and c are different )
+a+=+1+
+b+=+72+
+c+=+-225+
+C+=+%28+-72+%2B-+sqrt%28+72%5E2+-+4%2A1%2A%28-225%29+%29%29+%2F+%282%2A1%29+
+C+=+%28+-72+%2B-+sqrt%28+5184+%2B+900%29%29+%2F+2+
+C+=+%28+-72+%2B-+sqrt%28+6084%29%29+%2F+2+
+C+=+%28+-72+%2B-+78%29+%2F+2+
+C+=+6%2F2+
+C+=+3+ ( can't use the negative square root )
The river flows at 3 km/hr
check:
(1) ++45+=+%28+15+%2B+3+%29%2At+
(1) +45+=+18t+
(1) +t+=+2.5+ hrs
and
(2) +45+=+%28+15+-+3+%29%2A%28+t+%2B+75%2F60+%29+
(2) +45+=+12t+%2B+15+
(2) +12t+=+30+
(2) +t+=+2.5+ hrs
OK
There may be an easier way to solve this-
I just don't know what it is