Algebra Puzzle – Challenge 39

Challenge:

Joe and Mark can finish a job together in 100 minutes. If Joe can do the job by himself in 5 hours, how many minutes does it take Mark to finish the job?

A- 120

B- 150

C- 180

D- 200

E- 220

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5 hours = 300 minutes. Use the formula: \(\frac{1}{a} + \frac{1}{b} = \frac{1}{t}\)
Where, a is the rate for the first person and b is the rate of the second person. Joe can finish the job in 5 hours (300 minutes) and they both can finish the job in 100 minutes.
\(\frac{1}{300} + \frac{1}{b} = \frac{1}{100} → \frac{1}{b} = \frac{1}{100} – \frac{1}{300}→ b = 150\)
150 minutes takes Mark to finish the job

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