Question

If the sum of the upstream and downstream speed of a fish is $82$ mph, and it travels $105$ m. upstrem in $3$ hr. Find the time taken by a boat to cover $126$ m downstream.

• A. $2.7$ hrs
• B. $2.8$ hrs
• C. $2.5$ hrs
• D. $2.68$ hrs

Answer 1

The correct option is D $2.68$ hrs

Let

Speed of boat in still water $=b$

Speed of still water $=w$

Then, we know that,

Speed of upstream, $U=boat-water$

Speed of downstream, $D=boat+water$

Given,

$U+D=82$

So,

$b-w+b+w=82$

$⟹2b=82$

and

$b=41kmph$

From the given data,

$41-w=\frac{105}{3}=35$

$w=6kmph$

Now,

$b+w=\frac{126}{t}$

$⟹41+6=\frac{126}{t}$

$⟹t=\frac{126}{47}=2.68hrs$