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# A person can swim in still water at 5m/s. He moves in river of velocity 3m/s, First down the stream next same distance up the steam the ratio of times takes are(A) 1:1(B) 1:2(C) 1:4(D) 4:1

Last updated date: 12th Aug 2024
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Hint: This could be simply solved by applying the basic formula of speed. The average speed is the distance per time ratio.
Formula used: Here, we will use the basic formula of speed, distance and time:
${{\text{V}}_{{\text{avg}}}}{\text{ = }}\dfrac{{\text{D}}}{{\text{T}}}$
Here, ${{\text{V}}_{{\text{avg}}}}$is the mean speed of the car
${\text{D}}$is the total distance travel
$T$is the travel time

We will start by considering the total distance to be${\text{d}}$,
For the downstream over the distance:
${{\text{v}}_{\text{m}}}{\text{ = 5m/s and }}{{\text{v}}_{\text{r}}}{\text{ = 3m/s}}$
Similarly, for the upstream over the distance:
${{\text{v}}_p}{\text{ = 5m/s}}$
${v_r} = 3m/s$
And also, we find the respective time:
${t_1} = \dfrac{d}{{5 + 3}} = \dfrac{d}{8}$
${t_2} = \dfrac{d}{{5 - 3}} = \dfrac{d}{2}$
Now, the ratios between the time:
$\dfrac{{{t_1}}}{{{t_2}}} = \dfrac{{\dfrac{d}{8}}}{{\dfrac{d}{2}}} = \dfrac{1}{4}$
Thus, we need to select the correct option.

The correct option is C.

Additional Information: Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
The first scientist to measure speed as distance over time was Galileo.

Note: It should always be kept in mind that there is a difference between speed and velocity. Just as distance and displacement have distinctly different meanings, same is the situation between speed and velocity. Velocity is a vector quantity that refers to the rate at which an object changes its position whereas speed is a scalar quantity that refers to how fast an object is moving. Velocity gives us a sense of direction whereas speed does not give any sense of direction. If the velocity is constant, which creates a horizontal line
For example: If the person is travelling at a constant speed of 3 miles per hour, we can find the distance travelled by multiplying the speed by the amount of time they are walking. So, the person travelled 6 miles in 2 hours.