Question 18535
Let the speed of the boat be x kmph
Distance upstream=25 km
Time=distance/speed=(25/x)hours
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Now when going downstream,
distance=25 km
Speed of boat=(x+5)kmph [Given in question]
time taken=distance/speed=25/(x+5) hours
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Now the time taken downstream was 10 minutes less than time taken upstream
10 minutes means (10/60)hours=(1/6)hours
This means that time taken taken to go downstream was less
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So we get,
(time upstream)-(time downstream)=10 minutes
{{{ (25/x)-(25/(x+5))=(1/6) }}}
Taking LCM,
{{{ (25(x+5)-25(x))/(x(x+5))=1/6 }}}
{{{ (25x+25(5)-25x)/(x(x+5))=1/6 }}}
{{{ (25(5))/(x(x+5))=1/6 }}}
Taking x(x+5) to the other side,
{{{ 25(5) = (x(x+5))/6 }}}
{{{ 25(5)(6) = x(x+5) }}}
{{{ 25(30) = x(x+5) }}}
Taking everything to the right hand side we get,
{{{ 0 = x^2 + 5x - 25(30) }}}
Factoring this quadratic we get,
{{{ x^2 - 25x + 30x -25(30) = 0 }}}
{{{ (x-25)(x+30) = 0 }}}
x=25,-30
Speed cannot be negative
Therefore,x=25 kmph
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So speed of the boat upstream was 25kmph
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Hope this helps,
Prabhat