A motor boat whose speed is 18 km/h in still water takes 1 hour

Q) A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Ans:

VIDEO SOLUTION

STEP BY STEP SOLUTION

It is given that,

Speed of motor boat = 18 km/hr
Distance travelled =24 km
Time taken to travel in upstream is 1 hour more than in downstream

We need to find out: Speed of the stream

Let’s consider Speed of the stream is X km/ hr

Now, we know that during upstream, stream flows opposite to the boat and hence net speed is difference of the two speeds.
Hence, Net speed in upstream S_U = 18 – X
The time taken to flow 24 km Upstream T_U = $\frac{24}{18 - X}$ ……. (i)

Similarly, during downstream, stream flows along the boat and hence net speed is sum of the two speeds.
Hence, Net speed in downstream S_D = 18 + X
The time taken to flow 24 km downstream T_D= $\frac{24}{18 + X}$ ……. (ii)

Given that, T_U– T_D = 1
$\therefore \frac{24}{18 - X} - \frac{24}{18 + X} = 1$
24 (18 + X) – 24 (18 – X) = (18 – X)(18 + X)
48 X = 324 – X2
X2 + 48 X – 324 = 0
(X + 54)(X – 6) = 0
X = – 54, X = 6
Since Speed’s value can not be negative, it means X $\neq$ -54, and hence X = 6