Time and Work
Math MCQs

Question :    If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?

Correct Answer  21 ³/₁₇ days or 21.176 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Emily = 40 days

And, the number of days to finish the same work by Justin = 45 days

Thus, the number of days to finish the work by Emily and Justin together = ?

Here,

∵ In 40 days the work done by Emily = 1

∴ In 1 day, the work done by Emily = ¹/₄₀ part

Similarly,

∵ In 45 days the work done by Justin = 1

∴ In 1 day, the work done by Justin = ¹/₄₅ part

Now, in 1 day, the work done by Emily and Justin together

= In 1 day work done by Emily + In 1 day the work done by Justin

= ¹/₄₀ + ¹/₄₅

= ^{9 + 8}/₃₆₀

= ¹⁷/₃₆₀ part of work

This means in 1 day, ¹⁷/₃₆₀ part of work is done by Emily and Justin working together.

Now, the number of days required to finish ¹⁷/₃₆₀ part of work by Emily + Justin working together = 1

∴ the number of days required to finish 1 work by Emily + Justin together

= ¹/_¹⁷/360

= 1 × ³⁶⁰/₁₇ = ³⁶⁰/₁₇ days

= 21 ³/₁₇ days = or 21.176 days

Thus, Emily and Justin working together will finish the work in 21 ³/₁₇ days = or 21.176 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 Emily = 40 days

And the number of days required to finish the same work by Justin = 45 days

Thus, the number of days required to finish the work Emily and Justin working together = ?

Here a = 40 days

And, b = 45 days

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

The number of days required to finish the work when Emily and Justin working together

= ^{40 × 45}/_{40 + 45} days

= ¹⁸⁰⁰/₈₅ days

= ^{1800 ÷ 5}/_{85 ÷ 5} = ³⁶⁰/₁₇ days

= 21 ³/₁₇ days or 21.176

Thus, Emily and Justin together will finish the work in 21 ³/₁₇ days or 21.176 days Answer

Similar Questions

(1) Charles can finish a work in 19 days. Christopher can finish the same work in 20 days while Daniel can finish the work in 21 days. How long will it take to finish it if they work together?

(2) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?

(3) Richard can finish a work in 13 days. Joseph can finish the same work in 14 days while Thomas can finish the work in 15 days. How long will it take to finish it if they work together?

(4) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(5) If Donna can finish the work in 42 days and Brandon can finish the same work in 47 days, then in how many days both can finish the work together?

(6) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

(7) 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?

(8) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

(9) Deborah can finish a work in 54 days. Rebecca can finish the same work in 59 days while Sharon can finish the work in 64 days. How long will it take to finish it if they work together?

(10) If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?