Question

A man can row 30 km upstream and 44 km downstream in 10 hours.He can also row 40 km upstream and 55 km downstream in 13 hours .The speed with the man can row in still water is.

Answer 1

Answer:

speed of boat= 8 km/h

speed of stream = 3 km/h

Step-by-step explanation:

let speed of boat = (x) km/h

and speed of stream = (y) km/h

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Answer 2

$\textsf{Let the Speed with the Man can row in still water be : M\;km\;per\;hour}$

$\textsf{Let the Speed of the Stream be : S\;km\;per\;hour}$

$\textsf{While rowing Upstream : As the Stream, opposes the Motion of the Boat}$

$\textsf{The Speed of Boat while Rowing Upstream will be :}$

✿  $\textsf{Speed with the Man can row in still water - Speed of the Stream}$

$\implies \textsf{Speed of the Boat while rowing Upstream = (M - S)\;km\;per\;hour}$

$\textsf{While rowing Downstream : As the Stream, supports the Motion of the Boat}$

$\textsf{The Speed of Boat while Rowing Downstream will be :}$

✿  $\textsf{Speed with the Man can row in still water + Speed of the Stream}$

$\implies \textsf{Speed of the Boat while rowing Downstream = (M + S)\;km\;per\;hour}$

$\textsf{Given : The Man can row 30 km Upstream and 44 km Downstream in 10 hours}$

$\textsf{Time taken by the Boat to travel (M - S) km while rowing Upstream = 1 hour}$

$\sf{Time\;taken\;by\;Boat\;to\;travel\;30\;km\;while\;rowing\;Upstream = \bigg(\dfrac{30}{M - S}\bigg)\;hour}$

$\textsf{Time taken by the Boat to travel (M + S) km while rowing Downstream = 1 hour}$

$\sf{Time\;taken\;by\;Boat\;to\;travel\;44\;km\;while\;rowing\;Downstream = \bigg(\dfrac{44}{M + S}\bigg)\;hour}$

$\sf{\implies \bigg(\dfrac{30}{M - S}\bigg) + \bigg(\dfrac{44}{M + S}\bigg) = 10}$

$\sf{Let\;us\;take : \bigg(\dfrac{1}{M - S}\bigg) = P}$

$\sf{Let\;us\;take : \bigg(\dfrac{1}{M + S}\bigg) = Q}$

$\sf{\implies 30P + 44Q = 10}$

$\textsf{Multiplying above Equation with 4, We get :}$

$\sf{\implies 120P + 176Q = 40\;------\;[1]}$

$\textsf{Given : The Man can row 40 km Upstream and 55 km Downstream in 13 hours}$

$\sf{Time\;taken\;by\;Boat\;to\;travel\;40\;km\;while\;rowing\;Upstream = \bigg(\dfrac{40}{M - S}\bigg)\;hour}$

$\sf{Time\;taken\;by\;Boat\;to\;travel\;55\;km\;while\;rowing\;Downstream = \bigg(\dfrac{55}{M + S}\bigg)\;hour}$

$\sf{\implies \bigg(\dfrac{40}{M - S}\bigg) + \bigg(\dfrac{55}{M + S}\bigg) = 13}$

$\sf{\implies 40P + 55Q = 13}$

$\textsf{Multiplying above Equation with 3, We get :}$

$\sf{\implies 120P + 165Q = 39\;------\;[2]}$

$\textsf{Subtracting Equation [2] from Equation [1], We get :}$

$\sf{\implies (120P + 176Q) - (120P + 165Q) = 40 - 39}$

$\sf{\implies 120P + 176Q - 120P - 165Q = 1}$

$\sf{\implies 11Q = 1}$

$\sf{\implies Q = \dfrac{1}{11}}$

$\sf{\implies \dfrac{1}{M + S} = \dfrac{1}{11}}$

$\sf{\implies M + S = 11\;------\;[3]}$

$\sf{Substituting\;Q = \dfrac{1}{11}\;in\;Equation\;[1], We\;get :}$

$\sf{\implies 120P + \dfrac{176}{11} = 40}$

$\sf{\implies 120P + 16 = 40}$

$\sf{\implies P = \dfrac{24}{120}}$

$\sf{\implies P = \dfrac{1}{5}}$

$\sf{\implies \dfrac{1}{M - S} = \dfrac{1}{5}}$

$\sf{\implies M - S = 5\;-------\;[4]}$

$\textsf{Adding both Equations [3] and [4], We get :}$

$\sf{\implies M + S + M - S = 11 + 5}$

$\sf{\implies 2M = 16}$

$\sf{\implies M = 8}$

$\implies \textsf{Speed with the Man can row in still water = 8\;km\;per\;hour}$