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# A motorboat went down the river for 14 km and then up the river for 9

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Math Expert
Joined: 02 Sep 2009
Posts: 62532
A motorboat went down the river for 14 km and then up the river for 9  [#permalink]

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03 Jan 2020, 01:29
00:00

Difficulty:

55% (hard)

Question Stats:

76% (02:16) correct 24% (03:24) wrong based on 25 sessions

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A motorboat went down the river for 14 km and then up the river for 9 km. It took a total of 5 hours for the entire journey. Find the speed of the river flow if the speed of the boat in still water is 5 kmph.

A. 1 kmph
B. 1.5 kmph
C. 2 kmph
D. 2.5 kmph
E. 3 kmph

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Manager
Joined: 20 Aug 2017
Posts: 110
Re: A motorboat went down the river for 14 km and then up the river for 9  [#permalink]

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03 Jan 2020, 03:00
We are given the speed of boat as 5kmph and let speed of stream = X.
Now, we are given
$$\frac{14}{5+X} + \frac{9}{5-X} = 5$$
As we can see if we go on to solve the equation it will take a lot of time.
So we use options.
Option A: X = 1
Our equation becomes
$$\frac{14}{6} + \frac{9}{4} = 5$$

Now, $$\frac{14}{6}$$ results in a non terminating decimal. Eliminated

Option B: X = 1.5
Our equation becomes
$$\frac{14}{6.5} + \frac{9}{3.5} = 5$$

$$\frac{140}{65} + \frac{90}{35} = 5$$

$$\frac{28}{13} + \frac{18}{7} = 5$$
This too will result in non terminating decimals. Eliminated

Option C: X = 2
Our equation becomes
$$\frac{14}{7} + \frac{9}{3} = 5$$

$$2+3 = 5$$

We do not need to check further options.

OA, C

Bunuel wrote:
A motorboat went down the river for 14 km and then up the river for 9 km. It took a total of 5 hours for the entire journey. Find the speed of the river flow if the speed of the boat in still water is 5 kmph.

A. 1 kmph
B. 1.5 kmph
C. 2 kmph
D. 2.5 kmph
E. 3 kmph
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Location: India
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Re: A motorboat went down the river for 14 km and then up the river for 9  [#permalink]

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03 Jan 2020, 05:53
Bunuel wrote:
A motorboat went down the river for 14 km and then up the river for 9 km. It took a total of 5 hours for the entire journey. Find the speed of the river flow if the speed of the boat in still water is 5 kmph.

A. 1 kmph
B. 1.5 kmph
C. 2 kmph
D. 2.5 kmph
E. 3 kmph

Plugging in the options can work good for this one, the main equation is -

$$\frac{14}{5 + c} + \frac{9}{5 - c} = 5$$

Use option (C) 2

$$\frac{14}{5 + 2} + \frac{9}{5 - 2}$$

= $$\frac{14}{7} + \frac{9}{3}$$

= $$2 + 3$$

= $$5$$ , Answer must hence be (C)
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Senior Manager
Joined: 12 Sep 2017
Posts: 309
Re: A motorboat went down the river for 14 km and then up the river for 9  [#permalink]

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09 Jan 2020, 18:07
Hello uchihaitachi

Why did you get 5-X and 5+X?

Kind regards!
Manager
Joined: 20 Aug 2017
Posts: 110
Re: A motorboat went down the river for 14 km and then up the river for 9  [#permalink]

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09 Jan 2020, 19:09
It is the speed upstream and downstream.
The downstream speed = 5 + X
The upstream speed = 5 - X

jfranciscocuencag wrote:
Hello uchihaitachi

Why did you get 5-X and 5+X?

Kind regards!

Posted from my mobile device
Re: A motorboat went down the river for 14 km and then up the river for 9   [#permalink] 09 Jan 2020, 19:09
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