## 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