Answer to Riddle #88: Work Rate Puzzles
Philip Jones emailed me with the suggestion that I include a work-rate based puzzle and so I did:
The key to solving this kind of puzzle is to realise it's just a velocity calculation, or speed more accurately. Speed is distance over time.
In Bob's case for example he can do two fields in one hour. This is no different to 2 miles in 1 hour or 2mph. Adam can do 1 field in 1 hour.
Combined they can do 3fph (fields per hour,) so using our equations of motion, time equals distance over speed: they can mow 1 field in ⅓ of an hour, or 20 minutes.
Time for some more complicated problems
If one man can mow a wheat field with a scythe in four twelve-hour days and another man takes three such days, how long will it take them to mow the field working together?I promise not all of these will involve fields. So work out the speeds, add them, and solve for time.
Person 1: 1 field, 4 days, speed = ¼fpd
Person 2: 1 field, 3 days, speed = ⅓fpd
Adding the speeds 1/4 + 1/3 = 3/12 + 4/12 = 7/12
Time = distance over speed = 1 / (7/12) = 12/7 = 1 + 5/7 = 1 (12 hour,) day 8 hours 34 minutes 17.1429 seconds or 20 hours 34 minutes
If one man can paint a house in two days, another man can do it in 2.5 days at what rate would a third man have to paint houses for them, working together, to paint a house in a day?Person 1: 1 house, 2 days, speed = ½hpd
Person 2: 1 house, 2.5 days, speed = ⅖hpd
Person 3: 1 house, x days, speed = 1/xhpd
1 = 0.5 + 0.4 + 1/x
x = 10
It takes the third man 10 days to paint a house. Or, since I asked for the rate, he paints houses at a rate of 1 every 10 days
Both AI's did very well with this...
If you're curious what Bard made of this puzzle...
Bob can mow 2 fields in the same time, so he mows at a rate of 2 fields/hour.
Together, they mow at a rate of 1 + 2 = 3 fields/hour.
Therefore, it takes them 1/3 of an hour, or 20 minutes, to mow a field.
Here is the equation:
Combined rate = individual rate 1 + individual rate 2
Combined rate = 1 field/hour + 2 fields/hour
Combined rate = 3 fields/hour
Time = 1 field / 3 fields/hour
Time = 1/3 hour
Time = 20 minutes
If you're curious what ChatGPT made of this puzzle...
To mow one field, Adam can do it in 1 hour, which means his rate is 1 field per hour. Bob can mow 2 fields in 1 hour, so his rate is 2 fields per hour.
Working together, their combined rate is:
1 field per hour + 2 fields per hour = 3 fields per hour
Therefore, to mow one field, they will take:
1 field / 3 fields per hour = 0.33 hours = 20 minutes
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