Snehal can row 28 km downstream and 12 km upstream in 5 hours. He can row 21 km downstream an

Snehal can row 28 km downstream and 12 km upstream in 5...

Snehal can row $28 \mathrm{~km}$ downstream and $12 \mathrm{~km}$ upstream in 5 hours. He can row $21 \mathrm{~km}$ downstream and $10 \mathrm{~km}$ upstream in 4 hours. Find the speed of Snehal in still water. (1) $9 \mathrm{kmph}$ (2) $8 \mathrm{kmph}$ (3) $6 \mathrm{kmph}$ (4) $5 \mathrm{kmph}$

Snehal can row $28 \mathrm{~km}$ downstream and $12 \mathrm{~km}$ upstream in 5 hours. He can row $21 \mathrm{~km}$ downstream and $10 \mathrm{~km}$ upstream in 4 hours. Find the speed of Snehal in still water.
(1) $9 \mathrm{kmph}$
(2) $8 \mathrm{kmph}$
(3) $6 \mathrm{kmph}$
(4) $5 \mathrm{kmph}$

Key Concepts

Relative Speed in a Current

When an object moves in a fluid medium such as a river or air that has a current, its effective speed differs depending on whether it is moving with or against the current. Downstream or with the current, the effective speed is the sum of the object’s speed in still water and the speed of the current. Conversely, upstream, the effective speed is the difference between the object’s speed in still water and the speed of the current.

Time-Distance-Speed Relationship

The basic relationship between time, distance, and speed is foundational in problems of motion. It is expressed by the formula: time = distance/speed. This formula enables setting up equations where given distances and the times taken imply specific effective speeds, which can then be related to the object's speed in still water and the current's speed.

Systems of Equations

When multiple scenarios are provided, systems of equations can be set up to represent the different conditions. In such problems, each situation (for example, a trip involving both downstream and upstream movement) yields an equation based on the time-distance-speed relationship using effective speeds. Solving these systems simultaneously helps to find the unknown values, such as the speed in still water and the speed of the current.

Transcript

00:01 Here in the question it is being said that is neheltan road 28 kilometers downstream and 12 kilometer upstream in 5 hours so before beginning up let us see that the speed of the boat okay so let's see speed of the board bx okay so the speed of the board is equal to x kilometer per are okay and this is the speed of the boat in still water okay and the speed of still water speed of still water be y kilometer per hour so now another thing that you need to know is the downstream speed down stream speed is always given by x plus y and the upstream speed is always x minus y and the upstream speed is always x minus y this is just the basics so now we're here starting up with a question the first statement it's being said that snail can row 28 kilometers downstream and 12 kilometer upstream in 5 hours that means if you just use the formula of speed is equal to distance upon time or you can say time is equal to distance upon speed so from the first statement we'll get our first equation that is 28 upon x plus y plus 12 upon x minus y is equal to 5 since she is taking 5 hours in the same manner in the second statement it's being said that she can row 21 kilometers downstream and 10 kilometers upstream in 4 hours so that means the second statement will be the second equation sorry will be 21 upon x plus 5 plus 10 upon x minus y is equal to four right so now we've got two statements two equations over here now you can just put one upon x plus y equal to m and one upon x minus y equal to n so if you just do that the first equation can be reframed as 28m plus 12 n is equal to five and the second statement will be 21m plus 10 n equal to 4.

02:20 So now these are the two equations that we've got.

02:24 Now we just need to solve these two equations in order to find out the values of m and y.

02:29 So for that we'll be using the elimination method.

02:32 So now i'll be just multiplying the first equation by 10 and the second equation by 12.

02:38 So on doing that, what i'll get over here? the new equations will be 280m plus 120n is a little...

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