A can complete a task in 16 days and B is 4 times faster than A. Find the part of work done by both A and B together in 1 day.
A can complete a task in 16 days and B is 4 times faster than A. Find the part of work done by both A and B together in 1 day.
A$$\frac{5}{8}$$
B$$\frac{3}{16}$$
C$$\frac{5}{16}$$
D$$\frac{3}{20}$$
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correct answer is: option c) \( \frac{5}{16} \)
Explanation: First, find B's work rate. Since B is 4 times faster than A, B takes 1/4 the time A takes to complete the work.
Therefore B can complete the work in 16/4 = 4 days.
A's work rate is \( \frac{1}{16} \) per day, and B's work rate is \( \frac{1}{4} \) per day.
Together, their work rate is \( \frac{1}{16} + \frac{1}{4} = \frac{1}{16} + \frac{4}{16} = \frac{5}{16} \).
- Option a: \( \frac{5}{8} \) is incorrect. This value is much higher than what A and B can do together in a day.
- Option b: \( \frac{3}{16} \) is incorrect. This is not the correct sum of the individual work rates.
- Option c: \( \frac{5}{16} \) is correct. This is the sum of A's and B's work rate per day.
- Option d: \( \frac{3}{20} \) is incorrect. This value is obtained by the wrong calculation.
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