Question

Guddi's swimming speed in still water to the speed
of river is 7:1. She swims 4.2 km up the river in just
14 min. How much time will Guddi take to swim 18.4
km down the river?
12 minutes
11 minutes
23 minutes
46 minutes​

Answer 1

EXPLANATION.

Guddi's swimming speed in still water to the speed of river is = 7 : 1.

She swims 4.2 km up the river in just 14 minutes.

How much time will Guddi's take to swim 18.4 km down the river.

Let us considered that,

Speed in still water = x.

Speed in river = y.

Upstream speed = x - y.

Downstream speed = x + y.

Speed = Distance/time.

Guddi's swimming speed in still water to the speed of river is = 7 : 1.

⇒ x : y = 7 : 1.

⇒ x/y = 7/1.

⇒ x = 7y. - - - - - (1).

She swims 4.2 km up the river in just 14 minutes.

⇒ (x - y) = (4.2)/(14).

⇒ x - y = 0.3.

Put the value of equation (1) in this expression, we get.

⇒ 7y - y = 0.3.

⇒ 6y = 0.3.

⇒ y = 0.05 km/minutes.

How much time will Guddi's take to swim 18.4 km down the river.

⇒ (x + y) = (18.4)/(time).

Put the value of equation (1) and value of y in this expression, we get.

⇒ (7y + y) = (18.4)/(time).

⇒ 8y = (18.4)/(time).

⇒ 8 x 0.05 = (18.4)/(time).

⇒ 0.4 = (18.4)/(time).

⇒ time = (18.4)/(0.4).

⇒ time = (184)/(4).

⇒ time = 46 minutes.

∴ 46 minutes time will Guddi's take to swim 18.4 km down the river.

Option [D] is correct answer.

Answer 2

Answer:

$\: \boxed{\bf \: Time\:taken = 46 \: minutes \: }$

Step-by-step explanation:

Given that, Guddi's swimming speed in still water to the speed of river is 7:1.

Let assume that

Speed of swimming in still water = 7x km/min.

Speed of river = x km/min

So, Speed of upstream = 7x - x = 6x km/min

Now, Given that, She swims 4.2 km up the river in just

14 minutes.

It means,

Distance covered in upstream = 4.2 km

Time taken = 14 min

Speed of upstream = 6x km/min

We know,

$\sf \: Speed = \dfrac{Distance}{Time}$

$\sf \: 6x = \dfrac{4.2}{14}$

$\sf \: 6x = \dfrac{42}{140}$

$\sf \: x = \dfrac{7}{140}$

$\implies\sf \: x = \dfrac{1}{20}$

Now,

Speed of downstream = 7x + x = 8x km/min

Distance covered in downstream = 18.4 km

So,

$\sf \: Time\:taken = \dfrac{Distance}{Speed}$

$\sf \: Time\:taken = \dfrac{18.4}{8x}$

$\sf \: Time\:taken = \dfrac{18.4}{8} \times 20 \: \: \: \left[ \because \:x = \dfrac{1}{20} \right]$

$\sf \: Time\:taken = \dfrac{184}{80} \times 20 \:$

$\sf \: Time\:taken = \dfrac{184}{4} \:$

$\implies\sf \: \boxed{\bf \: Time\:taken = 46 \: minutes \: }$