Question

A boat travels 30 km upstream in a river in the same period of time as it takes to travel 50 km downstream. If the rate of stream is 5 kmph, find the speed of the boat in still water.

Answer 1

Hint- We will assume the speed of the boat is x. Since the rate of the stream is given in the question i.e. 5 kmph, we will add this speed of stream to the speed of the boat putting signs according to upstream and downstream.

Complete step-by-step answer:
So, let the speed of the boat that we have to calculate be $x$.
Now, as the boat travels upstream with speed $x$ and the rate of stream is 5 kmph, we will have-
Speed of boat in upstream: $\left( {x - 5} \right)$
As the boat travels downstream with speed $x$ and the rate of stream is 5 kmph, we will have-
Speed of boat in downstream: $\left( {x + 5} \right)$
Now, as we all know the formula of speed is-
$speed = \dfrac{d}{t}$ (Where d stands for distance and t stands for time)
So, from above formula, the formula for time will be-
$t = \dfrac{d}{s}$ (Where t stands for time, d for distance and s for speed)
Now, as the time period is given same, we will have:
$\dfrac{d}{s}$ (for upstream) = $\dfrac{d}{s}$ (for downstream)
$
   \Rightarrow \dfrac{{30}}{{x - 5}} = \dfrac{{50}}{{x + 5}} \\
    \\
   \Rightarrow 3x + 15 = 5x - 25 \\
    \\
   \Rightarrow 15 + 25 = 5x - 3x \\
    \\
   \Rightarrow 40 = 2x \\
    \\
   \Rightarrow x = 20 \\
$
Thus, the speed of the boat is 20 kmph.

Note: Always use the time distance formula in such questions. It is possible that they might change the units of measurements in the question such as km to m. in that case, change the unit from m to km first then solve the answer further or you will get stuck in between.