Question

Three workers are digging a ditch. They take turns working, and every one of them works for as long as it would take the other two to dig half of the ditch. They finished digging the ditch working in this manner. How many times faster would the three workers have finished digging the ditch if they had all been working at the same time?

Answer 1

The work would be finished 2.25 times faster if they had been doing the work at the same time.

Rate of doing work

Assumption;

• Provided each one of the workers works for an hour which is equivalent to the time it takes to finish half of the ditch.

In essence, the total time required to finish the ditch by 2 workers is; 2 hours.

• Hence, for 3 workers working simultaneously, the time required is 1hour 20 minutes. = 80 minutes

However, since they took 1 hour turns on the job, it follows that; The total time used is;

• Total time = 3 × 1hr = 3 hours = 180 hours

Hence they could have finished the work in;

• R = 180/80 times faster = 2.25 times faster.

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