Brain Teasers
The Sweaty Chef's Kebab Machine.
In the "Sweaty Chef Kebab shop" there are many workers, full time and part time.
Two of those workers are Bea O'Problem and Jaqueline Hyde. One day they were asked to clean out the well-used and grease-encrusted Kebab machine.
It would take Bea an hour to do the job on her own, but it would only take Jaqueline 45 minutes. If they worked together for the first 12 minutes, then Bea left to do something else (like scrape salad off the pavement outside the shop), how long would it take Jaqueline to finish the job on her own?
Two of those workers are Bea O'Problem and Jaqueline Hyde. One day they were asked to clean out the well-used and grease-encrusted Kebab machine.
It would take Bea an hour to do the job on her own, but it would only take Jaqueline 45 minutes. If they worked together for the first 12 minutes, then Bea left to do something else (like scrape salad off the pavement outside the shop), how long would it take Jaqueline to finish the job on her own?
Answer
Bea takes 60 mins to do a jobJaqueline takes 45 mins to do a job (both given)
In 12 mins, Bea does 12/60 = 1/5 = 3/15ths of the job
In 12 mins, Jaqueline does 12/45 = 4/15ths of the job
Thus in 12 mins 7/15ths of the job has been done, and thus there is 1-7/15 = 8/15ths left to do
So on her own, to complete 8/15ths of a job that would take her 8/15 x 45 = 24 mins
So it would take Jaqueline 24 mins to complete the rest of the job on her own
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Comments
Now this is a good problem. Working together for 12 mins is an interesting twist.
I like the concrete approach of say letting the Kebab Machine be 45 square metres (Big Kebabs).
B cleans 45 m in 60 mins or 3/4 m per minute.
J cleans 1 m /min.
Together the clean 1 and 3/4 m/min.
In 12 min together they clean 21 m leaving 24 m left to clean.
Therefoe takes J 24 mins.
I like the concrete approach of say letting the Kebab Machine be 45 square metres (Big Kebabs).
B cleans 45 m in 60 mins or 3/4 m per minute.
J cleans 1 m /min.
Together the clean 1 and 3/4 m/min.
In 12 min together they clean 21 m leaving 24 m left to clean.
Therefoe takes J 24 mins.
It was easy to do, much easier than the presented solution.
As you point out, Bea does 12/60 = 1/5 of the job. This means that Jaqueline does 4/5 of the job which will take her 4/5 * 45 = 36 minutes minus the 12 minutes already spent is 24 more minutes.
Seconds to do that way in your head and much less complicated.
As you point out, Bea does 12/60 = 1/5 of the job. This means that Jaqueline does 4/5 of the job which will take her 4/5 * 45 = 36 minutes minus the 12 minutes already spent is 24 more minutes.
Seconds to do that way in your head and much less complicated.
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