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

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(2) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?

(3) Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?

(4) If Mark can finish the work in 33 days and Jacob can finish the same work in 38 days, then in how many days both can finish the work together?

(5) If Thomas can finish the work in 18 days and Andrew can finish the same work in 21 days, then in how many days both can finish the work together?

(6) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?

(7) If Myra can finish the work in 25 days and Sophia can finish the same work in 15 days, then in how many days they both can finish the work working together?

(8) Emily can finish a work in 36 days. Donna can finish the same work in 37 days while Michelle can finish the work in 38 days. How long will it take to finish it if they work together?

(9) Brenda can finish a work in 76 days. Emma can finish the same work in 81 days while Nicole can finish the work in 86 days. How long will it take to finish it if they work together?

(10) If A can finish a work in 10 days and B can finish the same work in 15 days, then in how many days they both can finish the work working together?