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John can eat x doughnuts in y minutes. If Chen can eat doughnuts three

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John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 00:44
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John can eat x doughnuts in y minutes. If Chen can eat doughnuts three times as fast as John, how many doughnuts will John and Chen eat in an hour?

(A) \(15*\frac{4x}{4}\)

(B) \(60*\frac{3x}{y}\)

(C) \(15*\frac{16x}{y}\)

(D) \(60*\frac{x}{y}\)

(E) \(60*\frac{x}{3y}\)


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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 01:20
1
John can eat x doughnuts in y minutes.

Chen eats three time as fast as John

i.e. Chen can eat 3x doughnuts in y minutes.

i.e. Chen and John can eat (x+3x) = 4x donughnuts in y minutes

i.e. in 1 hour (60 minutes) they can eat (4x/y)*60 = 240x/y doughnuts every hour

i.e. 15(16x/y) doughnuts every hour

Answer: Option C
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 01:25
1
In Y mins, John eat doughnuts = X
so, in 1 min, John will eat = \(\frac{X}{Y}\)

Similarly, in 1 min, Chen will eat = \(\frac{3X}{Y}\) ... (eats Three times faster).

Together they will eat in 1 min = \(\frac{X}{Y}+\frac{3X}{Y}\) = \(\frac{4X}{Y}\)

So, in 1 hour (60 mins), they will eat - \(\frac{4X}{Y} * 60\) = \(240 * \frac{4X}{Y}\) which is equivalent to our option 'C' - \(15*\frac{16X}{Y}\)
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 03:30
1
John can eat (x/y) doughnuts in 1 minute. In an hour, he can eat 60*(x/y) doughnuts.

Chen can eat 3*(x/y) doughnuts in 1 minute. In an hour, he can eat 180*(x/y) doughnuts.

Together, they eat (60+180)*(x/y) = 240*(x/y) = 15*16*(x/y) doughnuts in an hour

FINAL ANSWER IS (C)

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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 04:34
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Quote:
John can eat x doughnuts in y minutes. If Chen can eat doughnuts three times as fast as John, how many doughnuts will John and Chen eat in an hour?

(A) 15∗4x/4
(B) 60∗3x/y
(C) 15∗16x/y
(D) 60∗x/y
(E) 60∗x/3y


r=td
john rate: x/y d/min
chen rate: 3x/y d/min
j+c 1 hr: 60min * (x/y+3x/y) = 60(4x/y) = 240x/y = 15(16x/y)

Ans (C)
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 05:20
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John can eat x doughnuts in y minutes
--> Number of doughnuts John can eat in 1 minute = \(\frac{x}{y}\)

Chen can eat doughnuts three times as fast as John
--> Number of doughnuts Chen can eat in 1 minute = \(3*\frac{x}{y} = \frac{3x}{y}\)

Number of doughnuts John & Chen can eat in 1 minute together = \(\frac{x}{y} + \frac{3x}{y} = \frac{4x}{y}\)

In 1 hour = 60 minutes = \(60*\frac{4x}{y} = 15*\frac{16x}{y}\)

Option C
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 07:52
1
John's rate: r=x/y
Chen's rate: r=3x/y
Combined rate: 4x/y

Solution: YummyDonuts = 60 * (4x/y) = 15 * (16x/y) <-- Recognizing that these two are the same is the tricky part I think.

Answer: C
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 09:58
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John: x doughnuts in y minutes
—> \(\frac{x}{y}\) —doughnuts per minute

Chen : \(3(\frac{x}{y})\)
Together in an hour:
—> \((\frac{x}{y}+ 3*\frac{x}{y})*60 = 240(\frac{x}{y})\)

Only answer choice C matches this answer ( \(15*\frac{16x}{y})\)

The answer is C

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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 24 Jan 2020, 20:51
1
John can eat x doughnuts in y minutes.
Rate of John = (x/y) min

If Chen can eat doughnuts three times as fast as John
Rate of Chen = 3x/y min

Using RT=W equation
Combined rate is 4x/y min

In 1 hour they will eat 4x/y * 60 = 240x/y

Checking the options
C is correct
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 25 Jan 2020, 01:23
1
Quote:
John can eat x doughnuts in y minutes. If Chen can eat doughnuts three times as fast as John, how many doughnuts will John and Chen eat in an hour?

(A) \(15∗\frac{4x}{4}\)

(B) \(60∗\frac{3x}{y}\)

(C) \(15∗\frac{16x}{y}\)

(D) \(60∗\frac{x}{y}\)

(E) \(60∗\frac{x}{3y}\)


John can eat x doughnuts in y minutes
=> The number of doughnuts John can eat in an hour is \(x*\frac{60}{y}\)
Chen can eat doughnuts three times as fast as John
=> The number of doughnuts Chen can eat in an hour is \(3x*\frac{60}{y}\)
=> The number of doughnuts John and Chen will eat in an hour is \(4x*\frac{60}{y} = 15∗\frac{16x}{y}\)
==>>> Choice C
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 25 Jan 2020, 09:08
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Ans: C

John in 1 min= x/y
Chen in 1 min=3x/y

so in 60 min= 60(x/y + 3x/y)=240 x/y= 15 16x/y
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 25 Jan 2020, 09:16
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2 methods;
method 1 :

Rate of John ; x/y and Rate of Chen ; 3x/y

in 60 mins they would be able to eat ; 4x/y * 60 = 240*x/y or say 15 * 16 x/y
IMO C

method 2
let rate of John be x=5 donuts per y= 30 mins ; i.e 10 donuts per hour
now rate of Chen would be 30 donuts per hour ;
total donuts eaten John + chen ; 40
substitute x & y in 15 * 16 * 5/ 30 ; IMO C;



John can eat x doughnuts in y minutes. If Chen can eat doughnuts three times as fast as John, how many doughnuts will John and Chen eat in an hour?
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 25 Jan 2020, 09:34
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John eats x/y donuts / minute
Chen eats 3x/y donuts /minute
Together they eat 4x/y donuts/minute = 60 * 4x/y = 15* 16x/y donuts / hour

IMO C

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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 25 Jan 2020, 14:51
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In y minutes, John can eat x doughnuts. Chen can eat 3x in y minutes.
Hence Chen and John can eat a total of 4x doughnuts in y minutes.
We are to determine how many doughnuts Chen and John can eat in 60 minutes. With the above information, we can reduce this question to a simple case of ratio and proportions.
y minutes : 4x
60 minutes : z
z=4x * 60/y = (15 * 16x)/y

The answer is C.
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three  [#permalink]

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New post 26 Jan 2020, 09:08
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John can eat doughnuts per minute = x/y
Chen can eat doughnuts per minute =3x/y, (As Chen can eat doughnuts three times as fast as John)
John and Chen eat doughnuts in one minute = x/y +3x/y = 4x/y
John and Chen eat doughnuts in an hour (60 minutes) = 4x*60/y = 240x/y = 15*16/y (15*16 =240)(C)
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Re: John can eat x doughnuts in y minutes. If Chen can eat doughnuts three   [#permalink] 26 Jan 2020, 09:08
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