Time and Work
Math MCQs

Question :    If Kimberly can finish the work in 35 days and Stephen can finish the same work in 39 days, then in how many days both can finish the work together?

Correct Answer  18 ³³/₇₄ days or 18.446 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kimberly = 35 days

And, the number of days to finish the same work by Stephen = 39 days

Thus, the number of days to finish the work by Kimberly and Stephen together = ?

Here,

∵ In 35 days the work done by Kimberly = 1

∴ In 1 day, the work done by Kimberly = ¹/₃₅ part

Similarly,

∵ In 39 days the work done by Stephen = 1

∴ In 1 day, the work done by Stephen = ¹/₃₉ part

Now, in 1 day, the work done by Kimberly and Stephen together

= In 1 day work done by Kimberly + In 1 day the work done by Stephen

= ¹/₃₅ + ¹/₃₉

= ^{39 + 35}/₁₃₆₅

= ⁷⁴/₁₃₆₅ part of work

This means in 1 day, ⁷⁴/₁₃₆₅ part of work is done by Kimberly and Stephen working together.

Now, the number of days required to finish ⁷⁴/₁₃₆₅ part of work by Kimberly + Stephen working together = 1

∴ the number of days required to finish 1 work by Kimberly + Stephen together

= ¹/_⁷⁴/1365

= 1 × ¹³⁶⁵/₇₄ = ¹³⁶⁵/₇₄ days

= 18 ³³/₇₄ days = or 18.446 days

Thus, Kimberly and Stephen working together will finish the work in 18 ³³/₇₄ days = or 18.446 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 Kimberly = 35 days

And the number of days required to finish the same work by Stephen = 39 days

Thus, the number of days required to finish the work Kimberly and Stephen working together = ?

Here a = 35 days

And, b = 39 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Kimberly and Stephen working together

= ^{35 × 39}/_{35 + 39} days

= ¹³⁶⁵/₇₄ days

= 18 ³³/₇₄ days or 18.446

Thus, Kimberly and Stephen together will finish the work in 18 ³³/₇₄ days or 18.446 days Answer

Similar Questions

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(2) If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?

(3) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

(4) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?

(5) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?

(6) Anna can finish a work in 74 days. Pamela can finish the same work in 79 days while Emma can finish the work in 84 days. How long will it take to finish it if they work together?

(7) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

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