Duo Work Time Calculation: John & Jesse Efficiency
This problem involves calculating the time required for two individuals, John and Jesse, to complete a task together, considering their differing efficiencies.
John's efficiency is given as 40% of Jesse's efficiency. Let $E_J$ represent John's efficiency and $E_{Je}$ represent Jesse's efficiency.
The relationship is mathematically expressed as: $E_J = 0.40 \times E_{Je}$
Calculate Total Work and Individual Efficiencies
To solve this efficiently, we can assign unit values to their efficiencies:
- Assume Jesse's efficiency $E_{Je} = 100$ units.
- Consequently, John's efficiency $E_J = 0.40 \times 100 = 40$ units.
- We know John completes the entire work alone in 35 days.
- The total amount of work can be calculated using the formula: Total Work = Efficiency $\times$ Time.
- Calculating the total work: $ \text{Total Work} = E_J \times \text{Time}_J = 40 \text{ units} \times 35 \text{ days} = 1400 \text{ units} $.
Determine Combined Efficiency and Time Taken Together
When John and Jesse work together, their individual efficiencies add up to give a combined efficiency.
- Combined Efficiency $E_{J+Je} = E_J + E_{Je}$.
- $E_{J+Je} = 40 \text{ units} + 100 \text{ units} = 140 \text{ units}$.
- The time needed for them to complete the work together is found by dividing the total work by their combined efficiency: $ \text{Time Together} = \frac{\text{Total Work}}{E_{J+Je}} $.
- Substituting the values: $ \text{Time Together} = \frac{1400 \text{ units}}{140 \text{ units/day}} = 10 \text{ days} $.
Thus, the duo will take 10 days to complete the work when collaborating.
Similar Questions
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Important Questions from Work Efficiency
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
