Arithmetic

Time, Speed & Distance

Medium

A man rows 20 km upstream and back again to the starting point in 110 minutes. If the speed of the stream is 2 kmph, then the speed of rowing in still water is

20 kmph

22 kmph

24 kmph

28 kmph

✅ Correct Option: 2

Let speed of rowing in still water = $x$ kmph

Upstream speed = $x - 2$ kmph (rowing speed $-$ stream speed)

Downstream speed = $x + 2$ kmph (rowing speed $+$ stream speed)

Time equation:

$\frac{20}{x-2} + \frac{20}{x+2} = \frac{110}{60}$ (because we have to convert minutes to hours)

$\frac{20(x+2)+20(x-2)}{(x-2)(x+2)}=\frac{110}{60}$

$\frac{20x+40+20x-40}{(x-2)(x+2)}=\frac{110}{60}$

$40x(60)=110(x-2)(x+2)$

$2400x=110(x^2-4)$ $[(a+b)(a-b)=a^2-b^2]$

$2400x=110x^2-440$

$110x^2 - 2400x - 440 = 0$

Solve quadratic:

$x = 22$ or $x = -0.2$ (reject negative)

Therefore, speed of rowing in still water is 22 kmph.

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Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from A at a speed of $5 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$ , reaches $B$ and comes back to $A$ at the same speed.

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Given below are two statements based on the following:

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours.

Statement I: Speed of the boat in still water is 12 km per hour.

Statement II: Speed of the stream is 4 km per hour.

In the light of the above statements, choose the correct answer from the options given below:

A man rows 20 km upstream and back again to the starting point in 110 minutes. If the speed of the stream is 2 kmph, then the speed of rowing in still water is

Solution

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