pedro and juan can do a piece of work in 3( 3)/(7) days. if pedro works in 3 days and juan in 4 days, they will finish the work. find the time required by each to do the work.
I thought you just said it takes Pedro 3 days, and Juan 4 days. I suspect something has been lost in translation.
Also, the notation 3 (3)/(7) is very unusual. Usually it is written as 3 3/7, unless you meant something else.
To find the time required by Pedro and Juan to complete the work individually, we can use the concept of their individual work rates. Let's assume that Pedro's work rate is P and Juan's work rate is J.
From the given information, we know that Pedro and Juan can complete the work in 3 (3/7) days. This means that their combined work rate is equal to 1 (since they complete the work together).
Since Pedro works for 3 days and Juan works for 4 days, we can calculate the amount of work they individually complete:
Pedro's work = Pedro's work rate × Pedro's time = P × 3
Juan's work = Juan's work rate × Juan's time = J × 4
Since they complete the work when Pedro works for 3 days and Juan works for 4 days, we can set up the equation:
Pedro's work + Juan's work = Total work
P × 3 + J × 4 = 1
Now, since Pedro and Juan can complete the work in 3 (3/7) days together, we can write another equation using their combined work rate:
Pedro's work rate + Juan's work rate = Combined work rate
P + J = 1 / (3 (3/7))
To solve these two equations simultaneously, we can use a substitution method. We know that P + J = 1 / (3 (3/7)), so we can substitute P in the first equation with this value:
(1 / (3 (3/7))) × 3 + J × 4 = 1
1 / (7/3) + J × 4 = 1
3/7 + J × 4 = 1
J × 4 = 1 - 3/7
J × 4 = 4/7
J = (4/7)/4
J = 1/7
Now substitute the value of J back into either of the original equations to find P:
P + J = 1 / (3 (3/7))
P + 1/7 = 1 / (3 (3/7))
P = 1 / (3 (3/7)) - 1/7
P = 1/ (10/3) - 1/7
P = 3/10 - 1/7
P = (3/10)*(7/7) - (1/7)*(10/10)
P = 21/70 - 10/70
P = 11/70
Therefore, Pedro requires 11/70 of the work to complete individually, and Juan requires 1/7 of the work to complete individually.