A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55km downstream. Find the speed of the boat in still water and the speed of the stream.
Answers
Explanation:
Let the speed of boat in still water=x km\hr and The speed of stream=y km\hr
Let the speed of boat in still water=x km\hr and The speed of stream=y km\hrSpeed of boat at downstream
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/hr
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
as , Time = distance/ speed
Time taken to cover 30 km upstream
⇒ 30/x-y
Time taken to cover 44km downstream
⇒ 44/x+y
According to first condition ,
⇒ 30/x-y = 44 / x+y = 10 .
Time taken to cover 40 km upstream
⇒ 40/x-y
Time taken to cover 55 km downstream
⇒ 55/x+y
According to second condition
⇒ 40 /x-y = 55 / x+y = 13 .
Let 1/x-y = u and 1/x+y = v
⇒ 30u + 44v = 10 .. eq 1
⇒ 40u + 55v = 13 .. eq 2
Multiplying eq 1 by 3 and eq 2 by 5 and substract both
⇒ (150u + 220v = 50 ) - ( 160u + 220v = 52 )
⇒ - 10u = -2 ⇒ u = 1/5
put u = 1/5 in eq 1
⇒30 × 1/5 +44v = 10 ⇒ 44v = 4, ⇒v = 1/4
⇒ u = 1/x-y = 1/5 ⇒x-y = 5 eq 3
⇒v= 1/x+y =1/7 ⇒x+y = 11 eq 4
by subtracting eq3 and eq4 ,we get ⇒x=8
put x= 8 in eq3 ⇒ y = 3 .
Hence, the speed of the boat in still water=8km\hr
Hence, the speed of the boat in still water=8km\hrThe speed of stream=3km\hr
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