## “Grocer and Draper” Country Store Conundrum

Here’s a neat little math brainteaser:

A country store owner had two rival assistants, who both prided themselves on their rapidity in serving customers. The young man on the grocery side of the store could weigh up 2 one-pound parcels of sugar per minute, while the young man on the drapery side of the store could cut 3 one-yard lengths of cloth in the same time. Their employer, one slow day, set them a race, giving the grocer a barrel of sugar and telling him to weigh up 48 one-pound parcels of sugar while the draper divided a roll of 48 yards of cloth into yard pieces. The two men were interrupted together by customers for 9 minutes, but the draper was disturbed 17 times as long as the grocer. What was the result of the race?

*Think you can figure this one out?! Submit your answers below in the comment section; will reveal answers in 24-48 hrs.
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More of our earlier math brainteasers here

RaLDoZ| Profile September 8th, 2008 - 12:03 amGrocer could weigh 2 one-pound parcel of sugar in one minute

so for 48 one pound parcels of sugar, he took 48/2 or 24 minutes

The Draper could cut 3 one-yard lengths of cloth in 1 minute

Since the 48 yard cloth was divided into yard pieces he had to cut only 47 times

He could cut 3 one yard cloth in 60 seconds so he’ll cut 2 one yard cloth in 40 sec

So total time taken by the draper = 15 minutes and 40 seconds

Now they both were disturbed for 9 minutes and the draper was disturbed 17 times more that the grocer

So x + 17x = 9

18x = 9

x = 1/2

so the grocer was disturbed for 1/2 minute and the draper was disturbed for 8 and a half minutes

Adding these values we get ->

Total time taken by grocer :

= 24 minutes + 1/2 minutes = 24 minutes 30 seconds

Total time taken by draper :

= 15 minutes 40 seconds + 8 minutes 30 seconds = 24 minutes 10 seconds

The Draper Won

falwan| Profile September 8th, 2008 - 2:23 am“but the draper was disturbed 17 times as long as the grocer”

could not quite understand what that meant!!

joe| Profile September 8th, 2008 - 5:11 amGiven it takes the grocer 1 minute to weight up 2 pounds of sugar, it would take him 24 minutes to do 48 pounds (48 divided by 2)

Likeswise the draper cuts 3 yards per minute so he will do 48 yards in 16 minutes (48/3).

Let g = time the grocer is interrupted

and d = time the draper is interrupted

Using smultaneous equations on the information:

g + d = 9 minutes Total interrupted time)

d = 17 g min How much longer the draper is interr.)

Solving gives g= 1/2 minute d= 8 1/2 minutes

So the grocer finishes after 24 + 0.5 minutes = 24.5 min

and the draper finishes after 16 + 8.5 min = 24.5 min

Therefore the answer is that they both finish at the same time. It is a tie!

Mashplum| PUZZLE MASTER | Profile September 8th, 2008 - 5:33 amTie.

suineg| PUZZLE MASTER | Profile September 8th, 2008 - 8:48 amI think the result is a tie; explanation:

GG= grocery guy pace; DG= Drapery guy pace

GG= 2 one pounds per minute

DG= 3 one yard per minute

TIME WIHTOUT INTERRUPTION:

GG= 48/2= 24 MINUTES

DG=48/3=16 MINUTES

INTERRUPTION TIME:

GGT + DGT = 9MINUTES

GGT= 1/18* 9= 0.5 MINUTES

DGT= 17/18*9= 8.5 MINUTES

TOTAL TIME:

GG= 24+0.5= 24.5 MINUTES

DG= 16 + 8.5= 24.5 MINUTES

SO BOTH GUYS TAKE THE SAME TIME, ITS A TIE; BUT DG IS MORE EFFICIENT IN WORKING TIME AND GG DEAL MORE EFFECTIVELY WITH CLIENTS JAJAJA

Shawn| PUZZLE GRANDMASTER | Profile September 8th, 2008 - 8:57 amContest ends in a tie. Such devoted employees!!

yash_opened| Profile September 8th, 2008 - 12:15 pmThey both finish at the same time, and take 24 1/2 minutes…….

michaelc| Profile September 8th, 2008 - 2:36 pmIt looks to me like they would tie.

9 minutes for both, and draper 17 times longer, means the grocer paused 1/2 minute and the draper 8 1/2 minutes.

So each took 24 1/2 minutes, unless there is a sneaky something going on in this one…

Nothing I can see. They tie.

kkfox| Profile September 9th, 2008 - 1:27 amThe race was a tie, both men finishing at 24.5 minutes (the draper needed 16 minutes to do his work and was delayed for 8.5 minutes, the grocer needed 24 minutes to do his work and was delayed for 0.5 minutes).

SoloSalsa| Profile September 9th, 2008 - 9:15 amWithout distraction, the grocer would finish in twenty-four minutes, and the draper in sixteen minutes.

The grocer was distracted for thirty seconds, but the draper spent eight and one half minutes with the customers.

It’s a draw: the grocer and the draper both took twenty-four and one half minutes to complete the tasks.

RK| Founder | Profile September 9th, 2008 - 2:14 pmAre we sure it ends in a tie?! Almost all answers submitted had this, but there’s a bit of a trick to the question…

(Raldoz was the only one so far that got this one correct)

michaelc| Profile September 9th, 2008 - 4:23 pmAha RK!

I expected treachery!

Perhaps it’s the draper. He could always fold some of the peices into, and make twice the cuts.

Or perhaps the way he wins is by leaving the last yard cut strategically without having to cut the last yard, and thus gaining in time that way.

Still perhaps it’s the wording of the problem. “One Yard Lengths” is pretty vague. Cloth is usually measured by “square yards”. So if the main piece of cloth is 48 square yards, and the draper can cut a length of 3 yards, instead of cutting 3 square yard pieces, could be the plot?

In this case we would need to know the length and width of the 48 square yard piece. 1’x48′ would require 47 -1 yard cuts. On the other hand a 2’x24′ piece would require 70- 1 yard cuts.

Ok, I give up. What’s the official answer?

suineg| PUZZLE MASTER | Profile September 9th, 2008 - 4:31 pmI think I saw what was my mistake; Raldoz has to be a genius for not be misleading by this: if you had 48 yards of cloths you dont have to cut the borders]; suppose it was 48 yards * 1 yards= 48 yards2; you really have to imagine the extreme together and you know you save 1 min, the drapery because for you to divide 38 units of cloths has to made only 47 cuts; so the drapery gets 23.5 minutes vs 24.5 minutes that the grocery guy take; drapery wins

suineg| PUZZLE MASTER | Profile September 9th, 2008 - 4:32 pm48 units I mean in my previous comment

suineg| PUZZLE MASTER | Profile September 9th, 2008 - 4:54 pmyou got me the first time with this one RK jaja a roll thats the magic trick word

suineg| PUZZLE MASTER | Profile September 9th, 2008 - 5:10 pmAnother answer going beyond the fact that you save one minute could be this “out of the box” answer:

“overlapping the fabriq”:

2 of 24= 8 minutes will it take

4 of 12= 4 minutes will it take

and so on; I know… the tool of cutting has limits, however there was not a restriction in the problem for that, and its a competition, anything goes.

drapery still wins jajaja cool.

RK| Founder | Profile September 9th, 2008 - 6:10 pmEven the best and brightest can get tripped up from time to time

@Michaelc- “I expected treachery!”, almost fell off my chair laughing :lol:

suineg| PUZZLE MASTER | Profile September 9th, 2008 - 10:03 pmI get it the second time;> only thing missed was divide the minute /3 ups jaja; how about the overlapping answer, could it be?; if a roll could be 2 * 24 not 1*48; and then you get different times depending in what was the configuration that the drapery guy usually used for is cuts; and still wins but I think with a better advantage, cool puzzle.

michaelc| Profile September 10th, 2008 - 8:36 am“while the draper divided a roll of 48 yards of cloth into yard pieces”

I have to point out that it’s not exactly clear how the 48 yard roll is displaced. It could be 1 yd x 48 yds, in which the draper would win, with 47 cuts. (One could point out the same advantage for the sugar weigher. When he weighs 47 lbs of sugar, he knows the last of it should be 1 lb.)

A 2 yd x 24 yd piece of cloth would provide the draper with no apparent advantage. 70 “one-yard” cuts to cut out the 48 “square yds”.

Nit picky, nit picky, you might say.

suineg| PUZZLE MASTER | Profile September 10th, 2008 - 9:49 amNice one MichaelC, he knows the last is 1 lb but I think he still needs to get the remaining 1 lb of sugar out of the big bag; nedding an extra time that the drapery guy does not need, second maybe but still some time greater than 0;

I have a question regarding the advantage issue; I agree with MichaelC that the drapery does not get an advantage if 3 one yard cloth means three cuts of 1 yard;

but what happen if that means to get three pieces of cloth of 1 square yard; in the case of the 48 *1; is the same because you only need tomake 1 cut in order to obtain 1 yard(square) of cloth but when you get for example: 3*16;

for the first three you have to make 5 cuts of 1 yard;so you would save 3 cuts at the end not 1 or 1 whole minute not 20 seconds, thats the advantage I was talking about, but maybe I saw the problem from a bad angle in the meaning of that phrase, cool.

suineg| PUZZLE MASTER | Profile September 10th, 2008 - 10:07 amone minute is wrong; maybe not a whole minute more exact would be:

60/5= 12 seconds per cut; saving 36 seconds; still 16 seconds advantage over the 20 seconds previous edge; sorry for my sloppyness in the comments in this puzzle. it does not neccessarily has to be uniform in every piece of one yard like the 3*16 configuration proves it; thats nice I think.