# If three doctors cure seven patients in five minutes, how long would it take for four doctors to cure three patients?

### 5 Answers

- TomVLv 71 year agoFavorite Answer
This is strictly an exercise in joint proportionality and ignores the real world aspects of Doctor-Patient relationships.. Hopefully, the number of cures (C) increases as the number of doctors (D) increases and as the length of time (T) increases. In other words, more doctors and more time yields more cures. Once you've assumed that the number of cures is jointly proportional to the number of doctors and the length of time, C = kDT, plug in the given number of cures (C = 7), Doctors (D = 3), and minutes (T= 5) and solve for k. Then use the value of k with the revised number of cures and doctors to find the time.

It's the exact same mathematical construct as "If 3 engineers can build 7 bridges in 5 months, how long would it take 4 engineers to build 3 sheds".

C = kDT

k = C/(DT) = 7/(3*5) = 7/15 (Cures per Doctor per Minute)

T = C/(kD) = 3/(7/15 * 4) = 45/28 minutes ≈ 1.607 min ≈ 1 min 36 sec

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- ComoLv 71 year ago
doctors____patients_____minutes

3___________7_________5

4___________3_______5 x 3/4 x 3/7

45/28 minutes = 1 . 6 mins = 1 min 36 sec

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- DWReadLv 71 year ago
3 doctors × 5 minutes = 15 doctor-minutes

(15 doctor-minutes)/(7 patients) = (15/7) doctor-minutes per patient.

3 patients × (15/7) doctor-minutes/patient = 45/7 doctor-minutes

45/7 doctor-minutes/(4 doctors) = 45/28 minutes ≅ 1 minute and 36 seconds

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- busterwasmycatLv 71 year ago
depends on if you use the fastest one or not. Cannot have fractional doctors or fractional patients so the normal methods for average rate calculation are not appropriate. I would have to assume that one doctor is faster than the other two so did three patients in five minutes rather than two as did the others. And then there is the very real issue that individual sickness is not identical between patients. Not a very realistic scenario, is what I am saying.

However, if you want to do the calculation for fun's sake, you have 15 work minutes from doctors (3x5 minutes), divided by 7 to give average patient care minutes, or 15/7 minutes of work is needed per patient.

New scenario : 15/7 minutes per patient times 3 patients = 45/7 work minutes, divided by 4 (doctors) = 22.5/7 (45/14) minutes per doctor, or 3 minutes plus 3/14 of a minute, or roughly 12 or 13 seconds. something along those lines. Not a realistic problem though.

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- Michael ELv 71 year ago
That depends on what the patients have. The time to cure a patient depends more on the illness than the number of doctors.

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