Question

A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is

Answer 1

Solution

• Total time taken would be 8/3 hrs

Given

• Total Time Taken in still water (T) = 2 hours

• Total Distance (S) = 16 Km

• Velocity of water = 4 km/h

To finD

• Time taken during the whole journey

Now,

Velocity of the Boat :

$\sf \: v = \frac{16}{2} \\ \\ \large{ \leadsto \: \sf \: v = 8 \: {kmh}^{ - 1}}$

Upstream

While going upstream,the water current is opposite to the motion of boat,their velocities are subtracted :

$\sf \: t_1 = \dfrac{8}{8 - 4} \\ \\ \dashrightarrow \: \sf \: t_1 = 2 \:h - - - - - (1)$

Downstream

Velocity of the water and boat are in the same direction

$\sf \: t_2 = \dfrac{8}{8 + 4} \\ \\ \dashrightarrow \: \sf \: t_2 = \dfrac{2}{3} \: h$

Total Time

$\sf \: T = t_1 + t_2 \\ \\ \longrightarrow \: \sf \: T = 2 + \dfrac{2}{3} \\ \\ \large{\longrightarrow \: \boxed{ \boxed{ \sf \: T = \dfrac{8}{3} h}}}$

Answer 2

$\huge{\underline{\mathfrak{\red{Answer}}}}$

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$\bold{\underline{\underline{\green{Given:-}}}}$

• Total Distance travelled

= 8km+8km = 16km

• Time taken to travel 16km = 2hours
• Velocity of water=4km /h

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$\bold{\underline{\underline{\blue{Need\:to\:Find:-}}}}$

Total Time taken to travel 8km upstream and 8km downstream =?

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$\huge{\underline{\mathbb{\red{SOLUTION}}}}$

Let,

speed of boat in still water = x km/hr

Speed of water = y km/ hr

given speed of water =4km/ hr

★Thus y= 4km/hr--------(i)

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Now it's given,

The boat goes 16km in 2hours

thus it's velocity in still water is:

$\frac{16km}{2hr}$

$\frac{16km}{2hr}$

${\boxed{\pink{Velocity\:in\:still\:water=8m/hr}}}$

★Thus x= 8km/hr---------(ii)

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The velocity of the boat in upstream = (x-y)km/ hr

》The velocity in upstream

= (8-4) km/hr ( from i and ii,x=8 and y=4)

= 4km/hr

Time taken by the boat to cover 8km upstream is:

$\frac{distance}{velocity}$

$= \frac{8km}{4km/ h}\\ = 2hr$

Thus,

${\boxed{\pink{Time\:taken\:to\:go\:upstream=\:2hour}}}$

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Velocity of boat in downstream is

=(x+y)km/hr

=(8+4)km/hr (from i and ii)

=12km/hr

Time taken by the boat to cover 8km downstream is:

$=\frac{distance}{velocity} \\ = \frac{8}{12} hr \\ = \frac{4}{6} hr \\ = \frac{2}{3} hr \\ = \frac{2}{3} \times 60min \\ = 2 \times 20min \\ = 40min$

${\boxed{\pink{Time\:taken\:to\:go\:Downstream=\:40min}}}$

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Thus total time taken

= Time taken to go upstream+ Time taken to go downstream

=2 hour+ 40 minutes

=2hour 40 minutes

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$\bold{\underline{\boxed{\red{Answer=\:2hour\:40minutes}}}}$