A boat goes 30km upstream and 44km downstream in 10 hrs. In 13 hrs,it can go 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat

Asked by joybasu274 | 13th Jan, 2018, 10:22: AM

Expert Answer:

begin mathsize 16px style Let space the space speed space of space the space boat space in space still space water equals straight x space km divided by hr space and space that space of space the space stream space equals straight y space km divided by kr
speed space upstream equals left parenthesis straight x minus straight y right parenthesis space km divided by hr
speed space downstream equals left parenthesis straight x plus straight y right parenthesis space km divided by hr
Time space taken space to space cover space 30 space km space upstream equals fraction numerator 30 over denominator straight x minus straight y end fraction space hours
Time space taken space to space cover space 44 space km space downstream equals fraction numerator 44 over denominator straight x plus straight y end fraction space hours
Total space time space of space journey equals 10 space hours
rightwards double arrow fraction numerator 30 over denominator straight x minus straight y end fraction space plus fraction numerator 44 over denominator straight x plus straight y end fraction equals 10

Time space taken space to space cover space 40 space km space upstream equals fraction numerator 40 over denominator straight x minus straight y end fraction space hours
Time space taken space to space cover space 55 space km space downstream equals fraction numerator 55 over denominator straight x plus straight y end fraction space hours
Total space time space of space journey equals 13 space hours
rightwards double arrow fraction numerator 40 over denominator straight x minus straight y end fraction space plus fraction numerator 55 over denominator straight x plus straight y end fraction equals 13

Putting space fraction numerator 1 over denominator straight x minus straight y end fraction equals straight u space and space fraction numerator 1 over denominator straight x plus straight y end fraction equals straight v comma space we space get
30 straight u plus 44 straight v equals 10 space space space space.... left parenthesis straight i right parenthesis
40 straight u plus 55 straight v equals 13 space space space space.... left parenthesis ii right parenthesis
You space can space solve space further space by space any space of space the space convenient space method space to space get space the space values space of space straight u space and space straight v.
Then space you space can space substitute space them space to space get space the space value space of space straight x space and space straight y.

Answer colon
Speed space of space stream equals 3 space km divided by hr
Speed space of space boat equals 8 space km divided by hr
end style

Answered by Rashmi Khot | 14th Jan, 2018, 02:46: PM