Multiple choice

A can do$ \dfrac{ 1 }{ 3 }$ of work in 5 days and B can do $\dfrac { 2 }{ 5 }$ of the work in 10 days.In how many days can both A and B together do the work?

  1. ${ 7 }_{ 4 }^{ 3 }$
  2. ${ 8 }_{ 5 }^{ 4 }$
  3. ${ 9 }_{ 8 }^{ 3 }$

  4. 10 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 1/3 in 5 days, so A takes 15 days for the whole work. B does 2/5 in 10 days, so B takes 25 days for the whole work. Combined rate = 1/15 + 1/25 = (5+3)/75 = 8/75. Time = 75/8 = 9 and 3/8 days.

AI explanation

A completes the entire work in 15 days, giving a work rate of 1/15 per day, and B completes the entire work in 25 days, giving a work rate of 1/25 per day. Using the combined work formula, their combined daily rate is 1/15 + 1/25 = 8/75 of the work per day. The reciprocal of this rate shows they will complete the work together in 75/8 days, which is 9 and 3/8 days.

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