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

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

Method: Change Factor

(R2/R1) * (T2/T1) = (W2/W1)

(6/22) * (x/9) = (1/1)
x = (22 *9)/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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Bunuel
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.

t takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour.
We can use this information to determine the distance to work
First we'll have to convert 9 minutes to 9/60 hours (simplify to get: 3/20 hours)

distance = (rate)(time)
So, distance = (22)(3/20 hours) = 66/20 = 33/10 miles

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?
time = distance/rate
So, time = (33/10)/6 = (33/10)(1/6) = 33/60 HOURS = 33 MINUTES

Cheers,
Brent
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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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Bunuel
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.

Given: It takes Carlos 9 minutes to drive from home to work at an average rate of 22 miles per hour.
Asked: 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?

D = s1 * t1 = s2 * t2 = 9 min * 22 mph = x min * 6 mph
x = 9 * 22/6 = 33 mins

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

T=9 mins Speed=22 miles/hr=22/60 miles/min

D=9*22/60

Therefore required T=D/S= 9*22/60/6/60=9*22/6=33 mins.

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Re: It takes Carlos 9 minutes to drive from home to work at an average rat [#permalink]
First converting 9 minutes into hours = 9/60 = 3/20
Distance = Rate / Time
D = 22 * 3/20 = 66/20 = 33/10

Minutes it will take Carlos cycle back home with the same route.

time = distance / rate
T = ( 33/10 ) / 6 = 33/ 10 * 1 / 6 = 33/60 = 33 minutes

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It takes Carlos 9 minutes to drive from home to work at an average rat [#permalink]
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Let the distance remain constant and since S1T1 = S2 T2 (distances being equal),we have

T2= D/S2

=S1 * T1 / S2 (Distance = Speed * Time)

= 22 * 9 / 6

= 33
(option b)
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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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Re: It takes Carlos 9 minutes to drive from home to work at an average rat [#permalink]
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