Question

Carpenter A takes 15 minutes to fit the parts of a chair while carpenter B takes 3 minutes more than A to do the same work. Working together, how long will it take for them to fit the parts for 22 chairs?

Answer 1

If A and B are working together then it will take 180 days for them to fit the parts for 22 chairs.

Step-by-step explanation:

Carpenter A takes 15 minutes to fit a chair

So, in 1 minute, the fraction of work done by A = $\frac{1}{15}$

Carpenter B takes 3 minutes more than A for the same work to be done i.e., B will take 15 + 3 = 18 minutes

So, in 1 minute, the fraction of work done by B = $\frac{1}{18}$

Therefore,

The fraction of work done by both A & B together in 1 minute will be,

= $\frac{1}{15} + \frac{1}{18}$

= $\frac{6+5}{90}$

= $\frac{11}{90}$

So, both A and B when working together will fit 1 chair in $\frac{90}{11}$ minutes

∴ To fit the parts of 22 chairs, A and B will take = $\frac{90}{11} * 22$ = 90 * 2 = 180 minutes

Thus, it will take 180 minutes for them to fit the parts for 22 chairs.

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