Three men took 7 days to paint the hull of a boat, how long would it have taken 5 men?

Please explain how to work outThree men took 7 days to paint the hull of a boat, how long would it have taken 5 men?
I think I remember this from High school, basically all you do is multiply 3*7=21 (';man-days';) then find a similar looking product on the right side so





3*7=5*x





(which is also equal to 21)





then you have





21=5*x





divide by 5 men





21/5= x days





(in other words it always takes the same amount of ';man- days';)





so the answer to your question would be 21/5 = 4.2 daysThree men took 7 days to paint the hull of a boat, how long would it have taken 5 men?
rate = one third boat per 7 days per man


(1 man * 7 days)/((1/3)boat) / (5 men) = 7*3/5 = 4.2 days
It looks to me lke the relationship is inversel proportional ie the more men you have the less days it takes. so to express this you can say 5 is directly proportional to 1 divided by 7





So 3: 1 divided by 7


So 3 : 0.14


dividing both sides by 3


= 1 : 0.05


Now multiplying both sides by 5 you get


5: 0.238





Now because it was inversely propprtional we have to find the recipricol of the answer, the easiest way to do this is to convert 0.238 into a faction which is 5 over 21. Now to simplyfy this so it is one over something divide 21 by 5. This leaves us with 1 divided by 4.2. And to find the recipricol of a fraction you just turn it upside down. ie 4.2 divided by 1 which is 4.2





So the answer is 4.2 days ( I Hope!)
The capacity of a 3 men to paint = 1/7 part per day





The individual capacity of a man = 1/7*3 = 1/21 part per day





The 5 men can complete = (1/21)*5 = 5/21 part per day





so 5 men can complete full painting = 1/(5/21) = 21/5 days
mt=mt (men*time)


So


3*7=5*t


Therefore


(3*7)/5=t


21/5=t


t=4.2 days
For 3 men, it takes 7 days to do the job. For 1 man, it would take 21 days. for 5 men, 21/5 days. 4.2 days.