Time and Work
Math MCQs

Question :    If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?

Correct Answer  19 ³⁵/₇₈ days or 19.449 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Emily = 37 days

And, the number of days to finish the same work by Justin = 41 days

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

Here,

∵ In 37 days the work done by Emily = 1

∴ In 1 day, the work done by Emily = ¹/₃₇ part

Similarly,

∵ In 41 days the work done by Justin = 1

∴ In 1 day, the work done by Justin = ¹/₄₁ 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

= ¹/₃₇ + ¹/₄₁

= ^{41 + 37}/₁₅₁₇

= ⁷⁸/₁₅₁₇ part of work

This means in 1 day, ⁷⁸/₁₅₁₇ part of work is done by Emily and Justin working together.

Now, the number of days required to finish ⁷⁸/₁₅₁₇ part of work by Emily + Justin working together = 1

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

= ¹/_⁷⁸/1517

= 1 × ¹⁵¹⁷/₇₈ = ¹⁵¹⁷/₇₈ days

= 19 ³⁵/₇₈ days = or 19.449 days

Thus, Emily and Justin working together will finish the work in 19 ³⁵/₇₈ days = or 19.449 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 = 37 days

And the number of days required to finish the same work by Justin = 41 days

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

Here a = 37 days

And, b = 41 days

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

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

= ^{37 × 41}/_{37 + 41} days

= ¹⁵¹⁷/₇₈ days

= 19 ³⁵/₇₈ days or 19.449

Thus, Emily and Justin together will finish the work in 19 ³⁵/₇₈ days or 19.449 days Answer

Similar Questions

(1) If Emily can finish the work in 37 days and Justin can finish the same work in 41 days, then in how many days both can finish the work together?

(2) If James can finish the work in 2 days and John can finish the same work in 6 days, then in how many days both can finish the work together?

(3) If Donald can finish the work in 35 days and Nicholas can finish the same work in 40 days, then in how many days both can finish the work together?

(4) If Susan can finish the work in 18 days and Donald can finish the same work in 23 days, then in how many days both can finish the work together?

(5) If Ashley can finish the work in 33 days and Eric can finish the same work in 36 days, then in how many days both can finish the work together?

(6) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?

(7) Sharon can finish a work in 60 days. Cynthia can finish the same work in 65 days while Kathleen can finish the work in 70 days. How long will it take to finish it if they work together?

(8) If Anna can finish the work in 74 days and Austin can finish the same work in 79 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?

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