Question

The sum of the speed of a boat in still water and the speed of the current is 10 kmph. If the boat takes 40 % of the time to travel downstream when compared to that of upstream, then find the difference of the speeds of the boat when travelling downstream and upstream​

Answer 1

Question -

The sum of the speed of a boat in still water and the speed of the current is 10km/h. If the boat takes 40% of the time to travel downstream when compared to that of upstream, then find the difference of the speeds of the boat when travelling downstream and upstream

Solution -

Let,

Speed of boat in still water = u

Speed of current =v

Hence,

u+v=10..............1)

If time up=t and time down =0.4t

Hence,

distance =(u-v)t = (u+v)(0.4)t

Or,

6u=14v

Or,

$3u = 7v \\ u = \frac{7v}{3} .........2)$

Substituting the value of u in equation 1 we will get -

$\frac{7v}{3} + v = 10$

$\frac{7v + 3v}{3} = 10$

$\frac{10v}{3} = 10$

$10v = 10 \times 3$

$v = \frac{10 \times 3}{10}$

$v = 3$

Now substituting the value of v in equation 2 we will get -

$u = \frac{7 \times 3}{3}$

$u = 7$

Speed in downstream = u+v = 7+3= 10 km/hr

Speed in upstream = u-v = 10-4= 6 km/hr

Therefore difference in speed = (10-4)=6km/hr

Answer 2

Answer:

Difference of the speeds of the boat when travelling downstream and upstream​ = 6km/hour

Step-by-step explanation:

Let the speed of the boat in still water = x km/hour

and let the speed of the current = y km/hour

Speed upstream =(x -y )km/hour

Speed downstream = (x+y)km/hour

Distance traveled =  speed × time taken

Let the distance traveled by boat in one direction = S

Time taken to travel upstream = $\frac{S}{x-y}$

Time taken to travel downstream = $\frac{S}{x+y}$

To find,

Difference of the speeds of the boat when travelling downstream and upstream​ = speed downstream - speed upstream

= x+y -(x-y)

= x+y-x+y

= 2y

∴ Required to find 2y

Given,

The sum of the speed of a boat in still water and the speed of the current is 10 kmph

That is, x+ y = 10km/h -------------(1)

The boat takes 40 % of the time to travel downstream when compared to that of upstream

Time  to travel downstream = 40% ×Time  to travel upstream

$\frac{S}{x+y}$ = 40% $\frac{S}{x-y}$ -----------------(2)

$\frac{1}{x+y}$ = $\frac{40}{100(x-y)}$

40(x+y) = 100(x-y)

40x+40y = 100x - 100y

60x = 140y

3x = 7y --------------(3)

(1)→x+ y = 10

3x + 3y = 30

From (3) we have 3x = 7y

7y + 3y = 30

10y = 30

y = 3km/hour

2y = 2×3 = 6km/hour

∴ Difference of the speeds of the boat when travelling downstream and upstream​ = 6km/hour

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