Time and Work
Math MCQs

Question :    If Kimberly can finish the work in 38 days and Stephen can finish the same work in 43 days, then in how many days both can finish the work together?

Correct Answer  20 ¹⁴/₈₁ days or 20.173 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kimberly = 38 days

And, the number of days to finish the same work by Stephen = 43 days

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

Here,

∵ In 38 days the work done by Kimberly = 1

∴ In 1 day, the work done by Kimberly = ¹/₃₈ part

Similarly,

∵ In 43 days the work done by Stephen = 1

∴ In 1 day, the work done by Stephen = ¹/₄₃ 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

= ¹/₃₈ + ¹/₄₃

= ^{43 + 38}/₁₆₃₄

= ⁸¹/₁₆₃₄ part of work

This means in 1 day, ⁸¹/₁₆₃₄ part of work is done by Kimberly and Stephen working together.

Now, the number of days required to finish ⁸¹/₁₆₃₄ part of work by Kimberly + Stephen working together = 1

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

= ¹/_⁸¹/1634

= 1 × ¹⁶³⁴/₈₁ = ¹⁶³⁴/₈₁ days

= 20 ¹⁴/₈₁ days = or 20.173 days

Thus, Kimberly and Stephen working together will finish the work in 20 ¹⁴/₈₁ days = or 20.173 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 = 38 days

And the number of days required to finish the same work by Stephen = 43 days

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

Here a = 38 days

And, b = 43 days

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

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

= ^{38 × 43}/_{38 + 43} days

= ¹⁶³⁴/₈₁ days

= 20 ¹⁴/₈₁ days or 20.173

Thus, Kimberly and Stephen together will finish the work in 20 ¹⁴/₈₁ days or 20.173 days Answer

Similar Questions

(1) If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?

(2) If Barbara can finish the work in 13 days and Anthony can finish the same work in 16 days, then in how many days both can finish the work together?

(3) 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?

(4) Michelle can finish a work in 40 days. Carol can finish the same work in 41 days while Amanda can finish the work in 42 days. How long will it take to finish it if they work together?

(5) If Kimberly can finish the work in 38 days and Stephen can finish the same work in 43 days, then in how many days both can finish the work together?

(6) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?

(7) If Jonathan can finish the work in 73 days and Sean can finish the same work in 78 days, then in how many days both can finish the work together?

(8) If Dorothy can finish the work in 47 days and Jack can finish the same work in 50 days, then in how many days both can finish the work together?

(9) If Myra can finish the work in 15 days and Sophia can finish the same work in 20 days, then in how many days they both can finish the work working together?

(10) William can finish a work in 15 days. Joseph can finish the same work in 20 days while Thomas can finish the work in 25 days. How long will it take to finish it if they work together?