Question

A boat travels 18km upstream in 6 hours. How long (in hrs) will it take to cover the same distance downstream. The speed of current is one fourth the speed of the boat in still water.
A. 3
B. 4
C. 3.6
D. 3.4

Answer 1

Hint: Upstream is always in the opposite direction of current and downstream I am always in a similar direction of current. So, speed of boat depends on still or moving water and this problem can be easily solved by using the basic formula such as speed = \[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\], speed(upstream) = speed of boat - speed of current, speed(downstream) = speed of boat + speed of current.

Complete step-by-step answer:
Let us assume that the speed of the boat is x km/hr
As we know from the question that the speed of the current is one-fourth of the speed of the boat.
So, speed of current is equal to \[\dfrac{1}{4} \times x = \dfrac{x}{4}\]km/hr
Let us first solve the speed of the boat during upstream.
As we know that,
Speed = \[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\] (1)
And Upstream speed = speed of boat – speed of current (2)
On comparing equation 1 and 2. We get,
\[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\] = speed of boat – speed of current
Now putting all the values in the above equation. We get,
\[\dfrac{{18}}{6} = x - \dfrac{x}{4}\]
By taking LCM in RHS of the above equation and then cross-multiplying. We get,
\[12 = 4x - x\]
12 = 3x
So, speed of boat = x = 4 km/hr
Now solving speed of current that is = \[\dfrac{x}{4}\] = \[\dfrac{4}{4}\] = 1 km/hr
Now let us solve the speed of the boat downstream.
Let the time taken by boat to travel downstream = t hours.
As we know that the downstream speed = speed of boat + speed of current (3)
On comparing equation 1 and 3. We get,
\[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\] = speed of boat + speed of current
\[\dfrac{{18}}{t} = x + \dfrac{x}{4}\]
As we know that the value of x = 4 km/hr
\[\dfrac{{18}}{t} = 4 + \dfrac{4}{4}\]
\[\dfrac{{18}}{t} = 5\]
Now cross-multiplying the above equation. We get,
\[t = \dfrac{{18}}{5}\] = 3.6 hours
So, the time taken by the boat to travel a 18km distance downstream will be equal to 3.6 hours.
Hence, the correct option will be C.

Note: Whenever we come up with this type of problem then first we have to assume the speed of the boat and then find the value of x using the equation speed in upstream = speed of boat - speed of current because we are given the time and distance travelled by boat in upstream. And after that we can find the time taken by boat in downstream by putting the value of x in the formula for speed of boat in downstream that is speed of boat + speed of current. This will be the easiest and efficient way to find the solution of the problem.