Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio . They accept a job which they can finish in days if they all work together for hours per day. However, Anu and Tanu work together for the first days, working hours minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio . They accept a job which they can finish in days if they all work together for hours per day. However, Anu and Tanu work together for the first days, working hours minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
Entered answer:
Solution
We have three workers with different speeds, and we need to find how long one of them takes to finish remaining work.
Given Information:
Time ratio for Anu : Tanu : Manu = 5 : 8 : 10
Working together, they can complete the job in 4 days (8 hours/day)
Anu and Tanu work together for 6 days (6 hours 40 minutes/day)
Find: Hours needed for Manu to complete remaining work
If time ratios are 5:8:10, then work rate ratios are
Let's assume individual times are 5k, 8k, and 10k hours respectively.
Work rates (efficiency):
Anu's rate = units per hour
Tanu's rate = units per hour
Manu's rate = units per hour
Using LCM helps us work with whole numbers instead of fractions, making calculations easier.
LCM of 5k, 8k, 10k = 40k
So if total work = 40k units:
Anu completes units per hour
Tanu completes units per hour
Manu completes units per hour
Combined rate = units per hour
Together they finish in hours
Total work = units
Therefore: , so
Time conversion: hours minutes =
hours
Work done by Anu and Tanu together:
Combined rate = units per hour
Time worked = hours
Work completed = units
Remaining work = units
Manu's rate = units per hour
Time needed = hours
Answer: 6
In work problems, we convert time ratios to rate ratios (reciprocals), use LCM for easier calculations, and always verify our answer makes sense with the given constraints.