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Example 19: A boat goes 30 km upstream and 44 km downstream in10 hours. In 13 hours, it can go40 km upstream and 55 kmdown-stream. Determine the speedof the stream and that of the boat instill water. |
| Answer» LET the speed of boat in still water=x km\hr and The speed of stream=y km\hrSpeed of boat at downstream⇒(x+y)km/hrSpeed of boat at upstream⇒(x−y)km/hr∵time=distance/speed Time taken to COVER 30 km upstream ⇒30/x−yTime taken to cover 44 km downstream⇒44/x+yAccording to the first condition,⇒30/x−y=44/x+y=10Time taken to cover 40 km upstream ⇒40/x−yTime taken to cover 55 km downstream ⇒55/x+yAccording to the second condition,⇒40/x−y=55/x+y=13Let 1/x−y=u and 1/x+y=v⇒30u+44v=10.....(eq1)⇒40u+55v=13.....(eq2)MULTIPLYING eq1 by 3 and eq2 by 5 and subtract both⇒(150u+220v=50)−(160u+220v=52)⇒−10u=−2⇒u=1/5put u=1/5 in (eq1)⇒30×1/5+44v=10⇒44v=4⇒v=1/11⇒u=1/x−y=1/5 ⇒ x−y=5...eq3⇒v=1/x+y=1/11 ⇒ x+y=11...eq4Subtracting eq3 and eq4, we get⇒x=8Put x=8 in eq3⇒y=3Hence, the speed of the boat in still water=8km\hrThe speed of stream=3km\hr | |