SOLUTION: The speed of a motor boat in still water is 60kph. It goes 100km up the river and then comes the 100km back in a total of 12 hours. what is the speed of the current of the river?

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Question 550396: The speed of a motor boat in still water is 60kph. It goes 100km up the river and then comes the 100km back in a total of 12 hours. what is the speed of the current of the river?
A caregiver earns Php150,000 a month in the USA. He spends 5% of his income for food, 10% for clothes, entertainment, and other miscellaneous items. He also spends 15% for the tuition fees of his children and 20% for food of his family in the Philippines. How much did he save for a month?
Found 2 solutions by josmiceli, mathstutor494:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
Let +t+ = the time for the upstream trip
You need an equation for going upstream ( against current )
and another equation for going downstream ( with current )
given:
Speed of boat in still water = +60+ km/hr
Speed of boat going upstream = +60+-+c+ km/hr
Speed of boat going downstream = +60+%2B+c+ km/hr
For both trips, +d+=+100+ km
-------------------------
Going upstream:
(1) +100+=+%2860+-+c%29%2At+ km
Going downstream:
(2) +100+=+%2860+%2B+c%29%2A%2812+-+t%29+ km
--------------------------
(1) +100+=+60t+-+c%2At+
and
(2) +100+=+720+%2B+12c+-+60t+-+c%2At+
I will make the substitution
+-60t+=+-120t+%2B+60t+
(2) +100+=+720+%2B+12c+-+120t+%2B+60t+-+c%2At+
Substitute (1) into (2)
(2) +100+=+720+%2B+12c+-+120t+%2B+100+
(2) +0+=+720+%2B+12c+-+120t+
(2) +120t+=+12c+%2B+720+
(2) +t+=+%281%2F10%29%2Ac+%2B+6+
--------------------
Substitute this into (1)
(1) +100+=+%2860+-+c%29%2A%28+.1c+%2B+6+%29+
(1) +100+=+6c+-+.1c%5E2+%2B+360+-+6c+
(1) +.1c%5E2+=+260+
(1) +c%5E2+=+2600+
(1) +c+=+50.99+
I'll say +c+=+51+
The speed of the current is 51 km/hr
check answer:
(1) +100+=+%2860+-+51%29%2At+
(1) +100+=+9t+
(1) +t+=+11.11+ hrs
and
(2) +100+=+%2860+%2B+51%29%2A%2812+-+t%29+
(2) +100+=+111%2A%2812+-+t%29+
(2) +100+=+1332+-+111t+
(2) +111t+=+1232+
(20 +t+=+11.099+
I think this is close enough since I rounded the answer
Look for a mistake on my part, because the current
is almost as fast as the boat in still water. He must
be on a very fast river!
----------------------
+.05+%2B+.1+%2B+.15+%2B+.2+=+.5+
he spent 50% and saved 50%
+150000%2A.5+=+75000+
He saved $75,000

Answer by mathstutor494(120) About Me  (Show Source):
You can put this solution on YOUR website!
Let speed of the current of the river be "x" kph
Hence time taken by motor boat up the river = 100/(60-x)
Similarly time taken by motor boat down the river = 100/(60+x)
Since total time taken by motor boat is 12 hrs, therefore
100/(60-x)+ 100/(60+x) = 12
Cross multiplying above eqn by the terms in denominator results in.....
{100*(60+x)}+ {100*(60-x)} = 12*(60+x)*(60-x)
>6000 +100x+6000-100x= 12(3600-x^2)
>12000 = 12(3600-x^2)
Dividing above eqn by 12...
> 1000 = 3600-x^2
Transposition results in
>x^2= 3600-1000
> x^2 = 2600
Therefore x = +-50.99 say 51
As the speed can not be -ve, therefore speed of the current of the river= 51kph