Problem:
A worker can finish the painting job in 15 days. Another worker can finish only 75% of that job for the same time. At first, the second worker painted for several days and then the first worker joined him and together they finished the rest of the work in 6 days. How many days each worker worked and what percent of the work has been done by each one of them.
Given:
Worker A finishes a paint job in 15 days
Worker B finishes only 75% of the paint job in 15 days
Asked:
a. Number of days each worker worked?
b. Percent of work done by each worker?
Solution:
LET: W – amount of work done; r – rate of work; t – duration of work
We know that, W = r x t Eq. 1
Plotting the given data, we have:
W 
r 
t 

Worker A (W_{A}) 
1 
15 days 

Worker B (W_{B}) 
75% or 3/4 
15 days 
Using Eq. 1, we get: r = W / t
Rate of W_{A} (r_{A}) = 1 / 15 = 1/15 per day
Rate of W_{B} (r_{B}) = ¾ / 15 = 1/20 per day
Total work done per day of W_{A} & W_{B} = r_{A} + r_{B }= 1/15 + 1/20 = 7/60 per day
Work done by W_{A} & W_{B} in 6 days = r_{A+B} x number of days = 7/60 x 6 days = 7/10
Portion of the paint job that W_{B} worked alone = 1 – W_{A+B} in 6 days = 1 – 7/10 = 3/10
Number of days W_{B} worked alone = W_{B} worked alone / Rate of W_{B} = 3/10 / 1/20 = 6 days
To solved for what is asked on (A), we get :
Number of days Worker A (W_{A}) worked = 6 days Ans.
Number of days Worker B (W_{B}) worked = 6 days + 6 days = 12 days Ans.
To solved for percent of work done by each worker (B):
W 
r 
t 

Worker A (W_{A}) 
1/15 per day 
6 days 

Worker B (W_{B}) 
1/20 per day 
12 days 
Work done of W_{A} = r_{A} x t_{A }= 1/15 x 6 days = 2/5 or 40% Ans.
Work done of W_{B} = r_{B} x t_{B} = 1/20 x 12 days = 3/5 or 60% Ans.