# Boats and Streams Questions

Q:

A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

 A) 1.8h B) 3h C) 4h D) 5h

Explanation:

Upstream speed = B-S

Downstream speed = B+s

B-S = 15/5 = 3 km/h

Again          B= 4S

Therefore    B-S = 3= 3S

=>             S = 1 and B= 4 km/h

Therefore    B+S = 5km/h

Therefore, Time during downstream = 15/5 = 3h

10 3839
Q:

A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river ?

$\inline&space;\frac{Time\:&space;taken\:&space;in\:&space;upstream}{Time\:&space;taken\:&space;in\:&space;downstream}$ = $\inline&space;\frac{2}{1}$

$\inline&space;\therefore$ $\inline&space;\frac{Downstream\:&space;speed}{upstream\:&space;speed}$ = $\inline&space;\frac{2}{1}$        where  $\inline&space;\frac{B+R}{B-R}=\frac{2}{1}$

B ---> speed of boat in still water

R---->speed of current

$\inline&space;\Rightarrow&space;\frac{B}{R}=\frac{3}{1}$    ( By componendo and dividendo)

$\inline&space;\Rightarrow&space;\frac{9}{R}=\frac{3}{1}\:&space;\:&space;\Rightarrow&space;R=&space;3\:&space;km/h$

3374
Q:

A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the string place is

 A) 16 km B) 18 km C) 21 km D) 25 km

Explanation:

Let the distance covered be D km.

$\inline&space;\frac{D}{10+4}+\frac{D}{10-4}=5$

$\Rightarrow&space;\frac{D}{14}+\frac{D}{6}=5$

$\inline&space;\Rightarrow&space;10D=&space;42\times&space;5=210$

$\inline&space;\Rightarrow&space;D=&space;21$  km

7 2762
Q:

A motor boat takes 12 hours to go downstream and it takes 24 hours to return  the same distance. what is the time taken by  boat in still water?

 A) 15 h B) 16 h C) 8 h D) 20 h

Explanation:

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by

$\inline&space;\frac{2\times&space;t1\times&space;t2}{t1+t2}=\frac{2\times&space;12\times&space;24}{36}=16h$

6 2143
Q:

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

 A) 5 kmph B) 10 kmph C) 15 kmph D) 45 kmph

Speed of the boat downstream  $\inline \fn_jvn \small s=\frac{d}{t}$ = $\inline \fn_jvn \small \frac{60}{3} = 20 kmph$
Speed of the boat upstream $\inline \fn_jvn \small s= \frac{d}{t} = \frac{30}{3} = 10 kmph$
$\fn_jvn&space;\small&space;\therefore$ The speed of the stream = $\inline \fn_jvn \small \frac{(speed of downstream - speed of upstream)}{2} = 5kmph$.