Time and Work
Math MCQs

Question :    If Jennifer can finish the work in 29 days and Joseph can finish the same work in 45 days, then in how many days both can finish the work together?

Correct Answer  17 ⁴⁷/₇₄ days or 17.635 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jennifer = 29 days

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

Thus, the number of days to finish the work by Jennifer and Joseph together = ?

Here,

∵ In 29 days the work done by Jennifer = 1

∴ In 1 day, the work done by Jennifer = ¹/₂₉ part

Similarly,

∵ In 45 days the work done by Joseph = 1

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

Now, in 1 day, the work done by Jennifer and Joseph together

= In 1 day work done by Jennifer + In 1 day the work done by Joseph

= ¹/₂₉ + ¹/₄₅

= ^{45 + 29}/₁₃₀₅

= ⁷⁴/₁₃₀₅ part of work

This means in 1 day, ⁷⁴/₁₃₀₅ part of work is done by Jennifer and Joseph working together.

Now, the number of days required to finish ⁷⁴/₁₃₀₅ part of work by Jennifer + Joseph working together = 1

∴ the number of days required to finish 1 work by Jennifer + Joseph together

= ¹/_⁷⁴/1305

= 1 × ¹³⁰⁵/₇₄ = ¹³⁰⁵/₇₄ days

= 17 ⁴⁷/₇₄ days = or 17.635 days

Thus, Jennifer and Joseph working together will finish the work in 17 ⁴⁷/₇₄ days = or 17.635 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 Jennifer = 29 days

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

Thus, the number of days required to finish the work Jennifer and Joseph working together = ?

Here a = 29 days

And, b = 45 days

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

The number of days required to finish the work when Jennifer and Joseph working together

= ^{29 × 45}/_{29 + 45} days

= ¹³⁰⁵/₇₄ days

= 17 ⁴⁷/₇₄ days or 17.635

Thus, Jennifer and Joseph together will finish the work in 17 ⁴⁷/₇₄ days or 17.635 days Answer

Similar Questions

(1) Kathleen can finish a work in 66 days. Angela can finish the same work in 71 days while Shirley can finish the work in 76 days. How long will it take to finish it if they work together?

(2) If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?

(3) 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?

(4) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?

(5) If Kevin can finish the work in 44 days and Frank can finish the same work in 47 days, then in how many days both can finish the work together?

(6) Benjamin can finish a work in 85 days. Gregory can finish the same work in 90 days while Alexander can finish the work in 95 days. How long will it take to finish it if they work together?

(7) Patricia can finish a work in 8 days. Linda can finish the same work in 13 days while Elizabeth can finish the work in 18 days. How long will it take to finish it if they work together?

(8) If William can finish the work in 12 days and Matthew can finish the same work in 16 days, then in how many days both can finish the work together?

(9) If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?

(10) Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?