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Working independently, Susan can perform a certain task in 6 hours and Tom can perform it in 7 hours. If Susan and Tom work together at the task for 3 hours, at which point Susan leaves, how many hours will it take Tom to complete the task alone?

Respuesta :

Answer:

0.5 hr = 30 minutes

Explanation:

Let the total amount of work to be done = 42 units

Thus, efficiency of Susan = 42 units / 6 hours = 7 units/hr

Efficiency of Tom = 42 units / 7 hours = 6 units/hr

They worked together for 3 hours, which means that total efficiency = 7 + 6 units/hr = 13 units/hr

Thus, Amount of work done = 13 units/hr * 3 hr  = 39 units

Amount of work left which must be completed by Tom alone = 42 - 39 units = 3 units

Thus, Time taken by Tom:

[tex]Time=\frac{3\ units}{6\ units/hr}=0.5\ hr[/tex]

Thus, Time taken by tom = 0.5 hr = 30 minutes