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CBSE Class 8 Answered

the speed of a boat in still water is 8 km/hr . it can go 15 km upstream and 22 km downstream in 5 hours. find the speed of the stream
Asked by susanta.rkl | 31 Aug, 2018, 10:42: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let comma
the space speed space of space the space stream space equals space straight x space km divided by hr
Speed space of space the space boat space in space still space water equals space 8 space km divided by hr
rightwards double arrow Speed space of space boat space minus space upstream space equals space open parentheses 8 space minus space straight x close parentheses space km divided by hr
and space Speed space of space boat space minus space downstream space equals space open parentheses 8 space plus space straight x close parentheses space km divided by hr
We space know space speed space equals space distance over time
rightwards double arrow time space equals space distance over speed
rightwards double arrow straight t subscript 1 open parentheses time space taken space by space the space boat space to space go space 22 km space down space stream close parentheses space equals space fraction numerator 22 over denominator 8 space plus space straight x end fraction space hr
and space straight t subscript 2 open parentheses time space taken space by space the space boat space to space go space 22 km space down space stream close parentheses space equals space fraction numerator 15 over denominator 8 space minus space straight x end fraction space hr
According space to space the space condition comma
straight t subscript 1 space plus space straight t subscript 2 space equals space 5
rightwards double arrow fraction numerator 22 over denominator 8 space plus space straight x end fraction space plus space fraction numerator 15 over denominator 8 space minus space straight x end fraction space equals space 5
rightwards double arrow fraction numerator 22 open parentheses 8 space minus space straight x close parentheses plus space 15 open parentheses 8 space plus space straight x close parentheses over denominator open parentheses 8 space plus space straight x close parentheses open parentheses 8 space minus space straight x close parentheses end fraction space equals 5
rightwards double arrow 176 space minus space 22 straight x space plus space 120 space plus space 15 straight x equals space 5 open parentheses 64 space minus space straight x squared close parentheses
rightwards double arrow space 5 straight x squared space minus space 7 straight x space space minus space 24 space equals space 0
rightwards double arrow space 5 straight x squared space minus space 15 straight x space space plus space 8 straight x space space minus space 24 space equals space 0
rightwards double arrow 5 straight x left parenthesis straight x space minus space 3 right parenthesis space plus space 8 left parenthesis straight x space minus 3 right parenthesis space equals space 0
rightwards double arrow left parenthesis straight x space minus space 3 right parenthesis open parentheses 5 straight x space plus space 8 close parentheses equals space 0
rightwards double arrow straight x space equals space 3 space or space space straight x space equals space fraction numerator negative 8 over denominator 5 end fraction
straight x space equals space fraction numerator negative 8 over denominator 5 end fraction space cant apostrophe straight t space ber space accepte. left parenthesis speed space is space not space negative right parenthesis
rightwards double arrow straight x space equals space 3
Therefore space the space speed space of space the space stream space equals space 3 km divided by hr

end style
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