A boat covers 14 kms in upstream and 20 kms downstream in 7 hours. Also it
covers 22 kms upstream and 34 kms downstream in 10 hours. Find the speed
of the boat in still water and of that the stream.

Asked by 6073sumant | 30th May, 2019, 09:17: AM

Expert Answer:

Let, the speed of a boat in still water = x km/hr
and speed of the stream = y km/hr
 
→ Speed of a boat in upstream = (x - y) km/hr and
Speed of a boat in downstream = (x + y) km/hr
 
We know that,
Time = Distance /Speed 
According to the conditions in the question, we get
 
begin mathsize 16px style fraction numerator 14 over denominator open parentheses straight x space minus space straight y close parentheses end fraction space plus space fraction numerator 20 over denominator straight x space plus space straight y space end fraction space equals space 7 space space space space space.... space left parenthesis straight i right parenthesis
fraction numerator begin display style 22 end style over denominator begin display style open parentheses straight x space minus space straight y close parentheses end style end fraction space plus space fraction numerator begin display style 34 end style over denominator begin display style straight x space plus space straight y space end style end fraction space equals space 10
rightwards double arrow space fraction numerator begin display style 11 end style over denominator begin display style open parentheses straight x space minus space straight y close parentheses end style end fraction space plus space fraction numerator begin display style 17 end style over denominator begin display style straight x space plus space straight y space end style end fraction space equals space 5 space space space space.... space left parenthesis ii right parenthesis
Let space fraction numerator begin display style 1 end style over denominator begin display style straight x space plus space straight y end style end fraction space equals space straight m space and space fraction numerator begin display style 1 end style over denominator begin display style straight x space minus space straight y end style end fraction space equals space straight n comma space we space get
14 straight m space plus space 20 straight n space equals space 7 space space space space.... space left parenthesis iii right parenthesis
11 straight m space plus space 17 straight n space equals space 5 space space space.... left parenthesis iv right parenthesis space
Multiply space Equation space left parenthesis iii right parenthesis space by space 11 space and space left parenthesis iv right parenthesis space by space 14 comma space we space get
154 straight m space plus space 220 straight n space equals space 77 space space space space.... space left parenthesis straight v right parenthesis
154 straight m space plus space 238 straight n space equals space 70 space space space space space..... left parenthesis vi right parenthesis
Subtract space left parenthesis straight v right parenthesis space from space left parenthesis vi right parenthesis comma space we space get
18 straight n space equals space minus space 7
rightwards double arrow straight n space equals space fraction numerator negative 7 over denominator 18 end fraction
Put space straight n space equals space fraction numerator begin display style negative 7 end style over denominator begin display style 18 end style end fraction space in space left parenthesis iii right parenthesis space comma space we space get
14 straight m space plus space 20 open parentheses fraction numerator begin display style negative 7 end style over denominator begin display style 18 end style end fraction close parentheses space equals space 7
rightwards double arrow straight m space equals space 133 over 126
fraction numerator begin display style 1 end style over denominator begin display style straight x space plus space straight y end style end fraction space equals space 133 over 126 space and space fraction numerator begin display style 1 end style over denominator begin display style straight x space minus space straight y end style end fraction space equals space fraction numerator begin display style negative 7 end style over denominator begin display style 18 end style end fraction
rightwards double arrow straight x space plus space straight y space equals space 126 over 133 space and space straight x space minus space straight y space equals space fraction numerator begin display style negative 18 end style over denominator begin display style 7 end style end fraction
Adding space both space the space equations comma space we space get
straight x space equals space fraction numerator negative 108 over denominator 133 end fraction space and space straight y space equals space 234 over 133
But space speed space of space the space boat space in space still space water space can apostrophe straight t space be space negative.
So space please space check space your space question. end style

Answered by Yasmeen Khan | 30th May, 2019, 11:14: AM