## Some Problems on Boats and Streams 1

1)A man can row upstream at 8kmph and downstream at 10kmph. Find the man’s rate in still water and the rate of current.
Solution : Rate in still water = 1/2 (10+8)km/hr = 9km/hr
Rate of current = 1/2(10-8)km/hr =1km/hr
2)A boat can travel with a speed of 12km/hr in still water . If the speed of the stream is 5km/hr , find the time taken by boat to go 68km downstream.
solution : Speed downstream = (12+5)km/hr  = 17 km/hr
Time taken to travel 68km downstream = 68/17hrs  =4hrs
3)If a man rows at the rate of 5kmph in still water and his rate against the current is 3.5kmph, then man’s rate along the current is ?
solutin : Let us consider the rate along the current be x kmph.
Then, 1/2(x+3.5) = 5  or X= 6.5 Kmph
4)A boat covers a certain distance downstream in 1 hour, while it comes back  in 3/2 hours. If the speed of the stream is 3kmph, what is the speed of the boaat in still water ?
Solution : Let the speed of the boat in still water be x kmph.
Then speed downstream = (X+3)kmph
Speed upstraem = (x-3)kmph
Therefore (X+3)*1 = (x-3)*3/2
2x+6=3x-9  => X= 15kmph
5)A speed of a boat in still water is 10 km/hr. If it can travel 26km downstream and 14km upstream in the same time , the speed of the stream is ?
solution : let the speed of the stream be x km/hr. then,
Speed downstream=(10+x)km/hr,
speed upstream= (10-x)km/hr
Therefore  26/(10+x)= 14/(10-x)
260-26x= 140+14x  => 40x=120
x=3km/hr