Danish can type 100 form letters in six hours. When Muneeb helps, they can do the job together in four hours. How long will it have taken when Muneeb to do the job if he works alone?

Explanation

Step 1: Define Work Rates

• Danish can type 100 form letters in 6 hours, so his work rate is: $$frac{100}{6} = frac{50}{3} text{ letters per hour}$$
• Together, Danish and Muneeb complete 100 letters in 4 hours, so their combined work rate is: $$frac{100}{4} = 25 text{ letters per hour}$$

Step 2: Define Muneeb's Work Rate

• Let Muneeb's work rate be $m$ (letters per hour).
  $$50/3+m=25$$
• Solve for $m$:
  m=25−50/3​ $$m = frac{75}{3} - frac{50}{3} = frac{25}{3} text{ letters per hour}$$

Step 3: Time Taken by Muneeb Alone

• Muneeb alone needs to type 100 letters, so the time required is: $$frac{100}{frac{25}{3}} = 100 times frac{3}{25} = 12 text{ hours}$$

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