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

Question

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.

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

davedekoos · Accepted Answer

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

Answer: B

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).

Rashad046 · Answer

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

gracie · Answer

let t=cycling time
6t=22*9
t=33 minutes

arturportugal · Answer

I did a little bit different:

6/22 = 9/x
6x = 198
x = 198/6 = 33

sasyaharry · Answer

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

Answer is  B

GMATGuruNY · Answer

\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

B

ScottTargetTestPrep · Answer

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,.

Answer: B

dabaobao · Answer

Method: Change Factor  
(R2/R1) * (T2/T1) = (W2/W1)

(6/22) * (x/9) = (1/1)
x = (22 *9)/6 = 33

ANSWER: B

BrentGMATPrepNow · Answer

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

Answer: B

Cheers, 
Brent

Kinshook · Answer

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

IMO B

hemantbafna · Answer

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.

B

Nipungupta9081 · Answer

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

Answer B

CrackverbalGMAT · Answer

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) 
D.S 
GMAT SME

Ashwi · Answer

does this approach applies only when speed units are same and time units are different?

how about when a) both speed and time have different units, and b)speed different units and time
 units are same?

Bunuel · Answer

You should understand what the formula means. It simply equates the same distance covered in two cases with two different speeds and respective times. To calculate the actual distance, speed and time must be in compatible units. However, to use the equality speed1 * time1 = speed2 * time2, the unit of speed is not required to match the unit of time, meaning that speed can be in miles per hour and time in seconds, because we’d be changing time on both sides proportionally. What matters is that the speed units match each other and the time units match each other.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards