Time and Work
Practice Problems
Answer: rk / Rate.
Method 1: Unitary Method (Work per day):
A's work rate per day = 1/10 of the work.
B's work rate per day = 1/15 of the work.
Combined work rate per day = A's rate + B's rate = (1/10) + (1/15)
Find a common denominator (LCM of 10 and 15 is 30):
Combined rate = (3/30) + (2/30) = 5/30 = 1/6 of the work per day.
Time taken together = 1 / (Combined rate) = 1 / (1/6) = 6 days.
Method 2: LCM Method (Assuming Total Work Units):
LCM of 10 and 15 is 30. Assume Total Work = 30 units.
A's efficiency (units per day) = Total Work / A's Time = 30 / 10 = 3 units/day.
B's efficiency (units per day) = Total Work / B's Time = 30 / 15 = 2 units/day.
Combined efficiency = A's efficiency + B's efficiency = 3 + 2 = 5 units/day.
Time taken together = Total Work / Combined Efficiency = 30 / 5 = 6 days.
Answer: They will complete the work together in 6 days.
Answer: Concepts Used: Finding individual rate from combined rate, calculating work done, calculating remaining work, finding time for remaining work.
Steps:
Find A's work rate per day:
Combined rate of A and B = 1/12 per day.
B's rate alone = 1/30 per day.
A's rate = (A+B)'s rate - B's rate = (1/12) - (1/30).
LCM of 12 and 30 is 60.
A's rate = (5/60) - (2/60) = 3/60 = 1/20 per day. (A alone takes 20 days).
Calculate work done by B in 5 days:
Work done by B = B's rate * Time = (1/30) * 5 = 5/30 = 1/6 of the work.
Calculate the remaining work:
Remaining work = Total Work - Work done by B = 1 - 1/6 = 5/6 of the work.
Calculate the time A takes to complete the remaining work:
Time = Remaining Work / A's rate = (5/6) / (1/20)
Time = (5/6) * 20 = 100/6 = 50/3 days.
Answer: A alone will complete the remaining work in 50/3 days (or 16 and 2/3 days).