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# It takes Carlos 9 minutes to drive from home to work at an average rat

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Math Expert
Joined: 02 Sep 2009
Posts: 53657
It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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17 Feb 2016, 06:12
5
8
00:00

Difficulty:

5% (low)

Question Stats:

91% (01:46) correct 9% (02:19) wrong based on 262 sessions

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It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26
(B) 33
(C) 36
(D) 44
(E) 48

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Joined: 23 Apr 2016
Posts: 2
Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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15 Jun 2016, 06:09
5
Bunuel wrote:
It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26
(B) 33
(C) 36
(D) 44
(E) 48

Kudos for correct solution.

I think the simplest way is hidden in the fact that the average speed from home to work in question is almost 4 times as less as the the one traveled at 22 miles per hour. Eventually, the time spent will be close but not equal to 4 * 9 min, which is 33
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Posts: 111
Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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17 Feb 2016, 14:18
2
3
There are a few approaches one could take to this problem, but since the numbers are a little awkward, I'm going to try to avoid as much calculation as possible. We could determine the distance travelled, then calculate the time it would take at 6 miles per hour, converting between minutes and hours, but there is a simpler way.

We know that $$distance = speed * time$$
We also know that in our problem the distance is constant. It is the same whether Carlos is driving or biking.

So $$distance = speed_1*time_1 = speed_2*time_2$$

What we're trying to find is the value of $$time_2$$, so $$time_2=\frac{speed_1*time_1}{speed_2}$$

$$time_2 = \frac{9*22}{6} = 33$$ minutes

Note that I did not have to convert the time into hours for this to work. The ratio of the times taken is the inverse ratio of the speeds, $$\frac{speed_1}{speed_2}=\frac{time_2}{time_1}$$ so since we are dealing with ratios, the units could be anything, and no conversion is necessary. If we actually needed to calculate the distance, then we would need to convert the time into hours (or the speed into miles per minute).
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It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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15 Jun 2016, 13:10
let t=cycling time
6t=22*9
t=33 minutes
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Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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05 Aug 2016, 04:02
I did a little bit different:

6/22 = 9/x
6x = 198
x = 198/6 = 33
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Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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23 Jun 2017, 16:32
1

Key is the distance being same

Let D1=R1XT1
Let D2=R2XT2

Since D1=D2, we can say R1T1=R2T2
$$T2=\frac{(R1XTI)}{R2}$$
$$T2=\frac{(22X9)}{6}$$
T2=33

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Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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26 Feb 2019, 06:12
Bunuel wrote:
It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26
(B) 33
(C) 36
(D) 44
(E) 48

$$\frac{new-rate}{old-rate} = \frac{6-mph}{22-mph} = \frac{6}{22} = \frac{3}{11}$$
Rate and time have a RECIPROCAL relationship.
Since the new rate is $$\frac{3}{11}$$ of the old rate, the new time must be $$\frac{11}{3}$$ of the 9-minute old time:
$$\frac{11}{3}(9) = 33$$ minutes

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Re: It takes Carlos 9 minutes to drive from home to work at an average rat  [#permalink]

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01 Mar 2019, 10:52
Bunuel wrote:
It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour. How many minutes will it take Carlos to cycle from home to work along the same route at an average rate of 6 miles per hour?

(A) 26
(B) 33
(C) 36
(D) 44
(E) 48

Kudos for correct solution.

Converting 9 minutes to 9/60 of an hour, we see that the distance to work is 9/60 x 22 = 3/20 x 22 = 3/10 x 11 = 33/10 miles.

Thus, it will take Carlos (33/10)/6 = 33/60 hours, or 33 minutes, to cycle to work,.

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Re: It takes Carlos 9 minutes to drive from home to work at an average rat   [#permalink] 01 Mar 2019, 10:52
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