Time and Work
Math MCQs

Question :    If Justin can finish the work in 79 days and Jesse can finish the same work in 84 days, then in how many days both can finish the work together?

Correct Answer  40 ¹¹⁶/₁₆₃ days or 40.712 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Justin = 79 days

And, the number of days to finish the same work by Jesse = 84 days

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

Here,

∵ In 79 days the work done by Justin = 1

∴ In 1 day, the work done by Justin = ¹/₇₉ part

Similarly,

∵ In 84 days the work done by Jesse = 1

∴ In 1 day, the work done by Jesse = ¹/₈₄ part

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

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

= ¹/₇₉ + ¹/₈₄

= ^{84 + 79}/₆₆₃₆

= ¹⁶³/₆₆₃₆ part of work

This means in 1 day, ¹⁶³/₆₆₃₆ part of work is done by Justin and Jesse working together.

Now, the number of days required to finish ¹⁶³/₆₆₃₆ part of work by Justin + Jesse working together = 1

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

= ¹/_¹⁶³/6636

= 1 × ⁶⁶³⁶/₁₆₃ = ⁶⁶³⁶/₁₆₃ days

= 40 ¹¹⁶/₁₆₃ days = or 40.712 days

Thus, Justin and Jesse working together will finish the work in 40 ¹¹⁶/₁₆₃ days = or 40.712 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 Justin = 79 days

And the number of days required to finish the same work by Jesse = 84 days

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

Here a = 79 days

And, b = 84 days

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

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

= ^{79 × 84}/_{79 + 84} days

= ⁶⁶³⁶/₁₆₃ days

= 40 ¹¹⁶/₁₆₃ days or 40.712

Thus, Justin and Jesse together will finish the work in 40 ¹¹⁶/₁₆₃ days or 40.712 days Answer

Similar Questions

(1) 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?

(2) George can finish a work in 51 days. Ronald can finish the same work in 56 days while Edward can finish the work in 61 days. How long will it take to finish it if they work together?

(3) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

(4) Samuel can finish a work in 87 days. Alexander can finish the same work in 92 days while Frank can finish the work in 97 days. How long will it take to finish it if they work together?

(5) Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?

(6) 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?

(7) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?

(8) Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?

(9) Donna can finish a work in 38 days. Michelle can finish the same work in 39 days while Carol can finish the work in 40 days. How long will it take to finish it if they work together?

(10) If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?