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
- 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?
- 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?
- 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.
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- 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:
- 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?
- 21 women can complete a task in 40 days. 30 men can complete the task in 21 days. What is the ratio of the number of days a man will take to complete the task alone to the number of days a woman will need to do that task?
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?
- Five women can do a work in thirty six days. If the ratio between the capacity of a man and a woman is 3:1, then find how many days it will take 5 men to complete the same work?
- If 15 persons can do a job in 30 days, then 30 persons with twice the efficiency can do the same job in how many days?
Important Questions from Work Efficiency
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?
