Question : If Timothy can finish the work in 53 days and Tyler can finish the same work in 58 days, then in how many days both can finish the work together?
Correct Answer 27 77/111 days or 27.694 days
Solution & Explanation
Solution
Given,
The number of days to finish the work by Timothy = 53 days
And, the number of days to finish the same work by Tyler = 58 days
Thus, the number of days to finish the work by Timothy and Tyler together = ?
Here,
∵ In 53 days the work done by Timothy = 1
∴ In 1 day, the work done by Timothy = 1/53 part
Similarly,
∵ In 58 days the work done by Tyler = 1
∴ In 1 day, the work done by Tyler = 1/58 part
Now, in 1 day, the work done by Timothy and Tyler together
= In 1 day work done by Timothy + In 1 day the work done by Tyler
= 1/53 + 1/58
= 58 + 53/3074
= 111/3074 part of work
This means in 1 day, 111/3074 part of work is done by Timothy and Tyler working together.
Now, the number of days required to finish 111/3074 part of work by Timothy + Tyler working together = 1
∴ the number of days required to finish 1 work by Timothy + Tyler together
= 1/111/3074
= 1 × 3074/111 = 3074/111 days
= 27 77/111 days = or 27.694 days
Thus, Timothy and Tyler working together will finish the work in 27 77/111 days = or 27.694 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, and B can finish the same work in b days,
then working together the number of days require to finish the work
= a × b/a + b days.
Here given,
The number of days required to finish the work by Timothy = 53 days
And the number of days required to finish the same work by Tyler = 58 days
Thus, the number of days required to finish the work Timothy and Tyler working together = ?
Here a = 53 days
And, b = 58 days
Thus, using formula a × b/a + b days
The number of days required to finish the work when Timothy and Tyler working together
= 53 × 58/53 + 58 days
= 3074/111 days
= 27 77/111 days or 27.694
Thus, Timothy and Tyler together will finish the work in 27 77/111 days or 27.694 days Answer
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