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
- A can do $\frac{1}{5}^{\text{th}}$ of some work in 12 days, B can do $20\%$ of the same work in 10 days, C can do $\frac{1}{6}^{\text{th}}$ of the work in 8 days and D can do $\frac{1}{5}^{\text{th}}$ of the work in 12 days. Who will complete the work first if all four started to work at the same time?
- A can do a certain work in 45 days. B is 50% more efficient than A, and C is 3 times as fast as A. They started the work together but C left 7 days before completion of the work. In how many days was the entire work completed?
Manoj is twice as efficient a fisherman as Anuraj, and together they complete a piece of work in 22 days. In how many days can Anuraj alone complete the same work?
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- Raju is thrice as good as a workman as Vinod and together they can finish a task in 21 days. In how many days can Vinod alone complete the work?
- If Raju is thrice as good workman as Ravi and takes 20 days less than him to complete a piece of work, then find the time taken by Ravi to complete the work.
- Kamal can complete a work in 14 days. Vimal is 40% more efficient than Kamal. The number of days Vimal will take to complete the same piece of work is:
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Important Questions from Work Efficiency
Sumi can complete a job working 5 hours per day in 2 days. If she doubles her working hours per day, then in how many days will she complete the work?
Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
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?
3 men working 7 hours a day can complete a piece of work in 45 days. In how many days will 9 men working 6 hours a day complete the same work?
