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.

Usernamevisible · Answer

Solution by KarishmaB

This question doesn’t seem that hard, conceptually speaking, but here is how my student attempted to do it: first, he saw that the time to complete the trip was given in minutes and the rate of the trip was given in hours so he did a simple unit conversion, and determined that it took Carlos (9/60) hours to complete his trip.

He then computed the distance of the trip using the following equation: (9/60) hours * 22 miles/hour = (198/60) miles. He then set up a second equation: 6 miles/hour * T = (198/60) miles. At this point, he gave up, not wanting to wrestle with the hairy arithmetic. I don’t blame him.

Watch how much easier it is if we remember our reciprocal relationship between rate and time. We have two scenarios here. In Scenario 1, the time is 9 minutes and the rate is 22 mph. In Scenario 2, the rate is 6 mph, and we want the time, which we’ll call ‘T.” The ratio of the rates of the two scenarios is 22/6. Well, if the times have a reciprocal relationship, we know the ratio of the times must be 6/22. So we know that 9/T = 6/22.

Cross-multiply to get 6T = 9*22.

Divide both sides by 6 to get T = 9*22/6.

We can rewrite this as T = (9*22)/(3*2) = 3*11 = 33, so the answer is B. This question is discussed HERE.

The other point I want to stress here is that there isn’t anything magical about rate questions. In any equation that takes the form a*b = c, a and b will have a reciprocal relationship, provided that we hold c constant. Take “quantity * unit price = total cost”, for example. We can see intuitively that if we double the price, we’ll cut the quantity of items we can afford in half. Again, this relationship can be exploited to save time.

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

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