# A race boat covers a distance of 60 km downstream in one and a half hour.It covers this distance upstream in 2 hrs. The speed of race boat in still water is 35 km/hr.Find the speed of the stream ?

Nov 28, 2016

$5$ km/hr

#### Explanation:

As the speed of the boat in still water is known to us we can calculate the speed of the stream either any stream i.e. down stream or up stream.

Say, the speed of the stream is $x$ km/hr.

Going downstream the speed of the boat and the speed of the stream will be added together i. e. $\left(35 + x\right)$ km/hr

Hence the boat goes $\left(35 + x\right)$ km in 1 hr.

For a distance of 60 km, the Time $= \frac{60}{35 + x}$hr

so, $\frac{60}{35 + x} = 1 \frac{1}{2} = \frac{3}{2}$

or, $3 \left(35 + x\right) = 2 \cdot 60$ [cross multiplication]

or, $105 + 3 x = 120$

or $3 x = 120 - 105$

or, $x = \frac{15}{3} = 5$

Speed of the stream is 5 km/hr.

Another way
Going upstream, the speed of the stream is deducted from speed of the boat i.e $\left(35 - x\right)$ km/hr

Hence goes $\left(35 - x\right)$ km in 1 hr.

Therefore for a distance of $60$ km Time = $\frac{60}{35 - x}$ hrs.

As per question, Time is 2 hours, so $\frac{60}{35 - x} = 2$

or $60 = 2 \left(35 - x\right)$ [ cross multiplication]

or, $60 = 70 - 2 x$

or $2 x = 70 - 60$

or, $x = \frac{10}{2} = 5$

So, speed of the stream is $5$ km/hr.

Dec 3, 2016

5 km/h

#### Explanation:

To solve this you only need one of the directions. That is; upstream or downstream. This is because you are given the speed of the boat in still water. Of you did not have the still water speed you would have to use both upstream and downstream.

Using ratio but in fraction FORMAT

For downstream we are given that:

$\left(\text{distance")/("time}\right) \to \frac{60 k m}{1.5 h}$

But we need the distance in 1 hour (speed or velocity)

$\left(\text{distance")/("time}\right) \to \frac{60 k m \div 1.5}{1.5 h \div 1.5} = \frac{40 k m}{1 h} \to 40 \frac{k m}{h}$

We are told that the speed of the boat in still water is $35 \frac{k m}{h}$

So the speed of the river has to be the difference between the two giving:

$\left(40 - 35\right) \frac{k m}{h} = 5 \frac{k m}{h}$

You normally see this written as 5 km/h