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If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:34) correct 30% (01:48) wrong based on 1271 sessions

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If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3,600,000x
Math Expert V
Joined: 02 Sep 2009
Posts: 65767
Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 15x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3600000x

X meters per second -->
--> 3,600X meters per hour (as there are 3,600 seconds in one hour);
--> 3,600X/1,000=18X/5 kilometers per hour (as there are 1,000 meters in one kilometer).

OR: if you are not comfortable with above manipulations with variable X then you can assume x to be equal to some #: let x=10.

Speed = 10 meters per second -->
--> 10*3,600=36,000 meters per hour -->
--> 36,000/1000=36 kilometers per hour.

So, if x=10, then y=36. Plug x=10 into the answer choices, the one which give 36 will be the correct answer:
A. 15x/18=150/18<36;
B. 6x/5=60/5=12;
C. 18x/5=36 correct choice;
D. 60x=600;
E. 3,600,000x=36,000,000.

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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If the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x? (1 kilometer=1000meters).

$$y*\frac{kilometers}{hour}=x*\frac{meters}{seconds}$$

$$y*\frac{1\;kilometer}{1\; hour}*\frac{1000 \;meters}{1 \;kilometer}*\frac{1\; hour}{3600 \;seconds}=x*\frac{meters}{seconds}$$

$$y*\frac{1000 \;meters}{3600 \;seconds}=x*\frac{meters}{seconds}$$ --------> $$y=\frac{3600}{1000}*x=\frac{18}{5}*x$$

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Math Expert V
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If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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3
x meters in 1 second i.e

$$\frac{x}{1000}$$ Kms in 1 Second i.e

$$\frac{x}{1000}$$ Kms in $$\frac{1}{60}$$ Minutes i.e

$$\frac{x}{1000}$$ Kms in $$\frac{1}{3600}$$ Hour i.e

$$\frac{x}{1000} * 3600$$ in 1 Hr = Y

$$y = \frac{18x}{5}$$

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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3
1
If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

In order to avoid the confusion in conversions, lets write this equation in its simplistic format.

$$x * \frac{Meters}{Second} = y * \frac{Kilometers}{Hour}$$

$$x * \frac{Meters}{Second} = y * \frac{Kilometers}{Hour} * \frac{(1000) Meters}{(1) Kilometer} *\frac{(1) Hour}{(60 * 60) Seconds}$$

Cancelling out the units - Kilometers and Hours on the R.H.S.

$$x * \frac{Meters}{Second} = y * \frac{(1000) Meters}{(3600) Seconds}$$

$$x * \frac{Meters}{Second} = y * \frac{(5) Meters}{(18) Seconds}$$

Lets take values in terms of y:

$$y * \frac{Meters}{Seconds} = x * \frac{Meters}{Second}* \frac{18}{5}$$

Which means:

$$y = \frac{18x}{5}$$

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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2
2
Hi All,

This question can be solved in a couple of different ways; you can use unit conversions or you can use TEST IT:

We're asked to convert X meters/second into Y kilometers/hour....

If X = 2, then...

2 meters/second =
120 meters/minute =
7200 meters/hour =
7.2 kilometers/hour

So we need an answer that equals 7.2 when X = 2

Plugging 2 into each of the answers gives us...

A) 10/18 = 5/9
B) 12/5 = 2.4
C) 36/5 = 7.2
D) 120
E) 7,200,000

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

We need to find an equation with x in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)

Speed = x/t
x meters/second
(3600) x meters/hour

Speed = y/t
y KM/hour
Speed = y(1000m)/hour

y(1000meters)/hour = (3600) x meters/hour

y(1000)/1hour = x(3600) / 1 hour
y(1000) = x(3600)
y = 3.6x

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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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Bunuel, is this a word problem or what tipe of problem is?
Do you have a link to find more of these problems, please?
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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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manalq8 wrote:
If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3600000x

There are 3,600 seconds in an hour and 1,000 meters in a kilometer. So, let’s convert y kilometers/hour to meters/second:

We can start by converting y kilometers to meters.

y kilometers = 1,000y meters

Next we can convert 1 hour to seconds.

1 hour = 3,600 seconds

Thus, y km/hr can be expressed as 1,000y/3,600 m/sec, or 5y/18 m/sec, after it’s simplified.

Since our two rates are equal, x = 5y/18. We need to solve this equation for y.

18x = 5y

18x/5 = y

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Math Expert V
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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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manalq8 wrote:
If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3,600,000x

Check other Conversion problems to practice in Special Questions Directory.
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Re: If the speed of X meters per second is equivalent to the speed of Y ki  [#permalink]

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1
manalq8 wrote:
If the speed of X meters per second is equivalent to the speed of Y kilometers per hour, what is Y in terms of X? (1 kilometer=1000 meters)

A. 5x/18
B. 6x/5
C. 18x/5
D. 60x
E. 3,600,000x

Y km/hr = Y 1000 / 60*60 m/s = 5Y/18 m/s = X m/s
Y = 18X/5

IMO C
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Email: kinshook.chaturvedi@gmail.com Re: If the speed of X meters per second is equivalent to the speed of Y ki   [#permalink] 08 Oct 2019, 09:06

# If the speed of X meters per second is equivalent to the speed of Y ki  