Time and Work
Math MCQs

Question :    If Stephanie can finish the work in 56 days and Adam can finish the same work in 61 days, then in how many days both can finish the work together?

Correct Answer  29 ²³/₁₁₇ days or 29.197 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Stephanie = 56 days

And, the number of days to finish the same work by Adam = 61 days

Thus, the number of days to finish the work by Stephanie and Adam together = ?

Here,

∵ In 56 days the work done by Stephanie = 1

∴ In 1 day, the work done by Stephanie = ¹/₅₆ part

Similarly,

∵ In 61 days the work done by Adam = 1

∴ In 1 day, the work done by Adam = ¹/₆₁ part

Now, in 1 day, the work done by Stephanie and Adam together

= In 1 day work done by Stephanie + In 1 day the work done by Adam

= ¹/₅₆ + ¹/₆₁

= ^{61 + 56}/₃₄₁₆

= ¹¹⁷/₃₄₁₆ part of work

This means in 1 day, ¹¹⁷/₃₄₁₆ part of work is done by Stephanie and Adam working together.

Now, the number of days required to finish ¹¹⁷/₃₄₁₆ part of work by Stephanie + Adam working together = 1

∴ the number of days required to finish 1 work by Stephanie + Adam together

= ¹/_¹¹⁷/3416

= 1 × ³⁴¹⁶/₁₁₇ = ³⁴¹⁶/₁₁₇ days

= 29 ²³/₁₁₇ days = or 29.197 days

Thus, Stephanie and Adam working together will finish the work in 29 ²³/₁₁₇ days = or 29.197 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 Stephanie = 56 days

And the number of days required to finish the same work by Adam = 61 days

Thus, the number of days required to finish the work Stephanie and Adam working together = ?

Here a = 56 days

And, b = 61 days

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

The number of days required to finish the work when Stephanie and Adam working together

= ^{56 × 61}/_{56 + 61} days

= ³⁴¹⁶/₁₁₇ days

= 29 ²³/₁₁₇ days or 29.197

Thus, Stephanie and Adam together will finish the work in 29 ²³/₁₁₇ days or 29.197 days Answer

Similar Questions

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(2) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?

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(6) If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?

(7) If John can finish the work in 28 days and Richard can finish the same work in 44 days, then in how many days both can finish the work together?

(8) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

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