a boat takes 4 hoursto go 44 km downstreaam and it can go 20 km upstrean in the same time.find the speed of boat and stream in still water
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Pawanpreet asked in Math
a boat takes 4 hoursto go 44 km downstreaam and it can go 20 km upstrean in the same time.find the speed of boat and stream in still water
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Bhavya Saraf answered this
112 helpful votes in Math, Class XI-Science
Let speed of boat in still water = xkmph
Let speed of stream be = y kmph
= Speed upstream = (x - y) kmph
Speed downstream = (x+y) kmph
Case 1. Downstream , distance = 44kms ; speed = x+ y kmph , time = 4hrs
time = distance/ speed
= t = 44/x+y = 4 = 44/(x+y) = 1/(x+y) = 1/11
= x+ y = 11kmph --------------- 1.
Case 2. Upstream distance = 20kms. ; speed = (x-y)kmph ; time = 4hrs
= t = 20/(x-y) = 4 = 20/(x-y) = 1/(x-y) = 1/5
= x - y = 5kmph ----------------------- 2.
Adding 1. and 2. , we get
x + y + x -y = 11 + 5
2x = 16 = x = 8kmph
x + y = 11 = 8 +y = 11kmph
= y = 3kmph
Hence speed of boat = 8kmph
Speed of stream = 3 kmph
let x = speed of boat and y = speed of stream
speed downstream = x + y and speed upstream = x - y, hence
x + y = 44/ 4 = 11 and x - y = 20/4 = 5 , solving we get
x = 8 and y = 3