Question

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.

Answer 1

Hint: Use the fact that speed of upstream is the difference of speed of boat in still water and speed of stream and speed of downstream is sum of speed of boat in still water. Then use the formula,
$\text{Time=}\dfrac{\text{Distance}}{\text{Speed}}$ and found according to the question.

Complete step-by-step answer:
In the question we are told about a motor boat whose speed is 18 km/hr, in still water it takes 1 hour more to go 24 km than to return downstream to the same spot. Now we have to find the speed of stream
As we are given, the speed of a boat in still water is equal to 18 km/hr. Let's suppose the speed of the stream is skm/hr.
So, as we know,
Speed of upstream = Speed of boat in still water – Speed of stream
which can be written as,
Speed of upstream = 18 – s
Now for downstream,
Speed of downstream = Speed of boat in still water + Speed of steam
which can be written as,
Speed of downstream = 18 + s
Now, according to question we are told,
Time taken for upstream = Time taken to cover downstream + 1
We can present,
$\Rightarrow \text{Time taken for upstream=}\dfrac{\text{Distance of upstream}}{\text{Speed of upstream}}$
and $\text{Time taken for downstream = }\dfrac{\text{Distance of downstream}}{\text{Speed of downstream}}$
We know that,
Distance of upstream and downstream is equal to 24 km so we can write equation as,
$\dfrac{24}{18-s}=\dfrac{24}{18+s}+1$
which we can write as,
$\dfrac{24}{18-s}-\dfrac{24}{18+s}=1$
Now taking LCM we get
$\dfrac{24\left( 18+s-18+s \right)}{324-{{s}^{2}}}=1$
On cross multiplication we get,
$48s=324-{{s}^{2}}$
which we can rewrite as,
${{s}^{2}}+48s-324=0$
Now using middle term factor, we get,
${{s}^{2}}-6s+54s-324=0$
Now on factoring we get,
$(s-6)(s+54)=0$
So, s is equal to 6 and – 54 as s represents speed so it can’t be negative. Hence, s is 6.
Hence, Speed of the stream is 6 km/hr.

Note: Students should know the relation between speed of upstream and downstream in terms of speed of boat in still water and speed of stream.