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'A' and 'B' can complete a work in 2 hours and 55 minutes. 'A' alone can do the same work two hours faster than 'B' alone can. How long will 'B' take to do the work alone ?
Explanation
Let the time taken by 'B' to complete the work alone be x hours. Therefore, the time taken by 'A' alone is (x - 2) hours.
The combined time taken by 'A' and 'B' is 2 hours and 55 minutes, which is 2 + 55⁄60 = 2 + 11⁄12 = 35⁄12 hours.
According to the work-rate formula:
1⁄(x - 2) + 1⁄x = 12⁄35
Solving the equation:
(2x - 2) / (x2 - 2x) = 12/35
35(2x - 2) = 12(x2 - 2x)
12x2 - 94x + 70 = 0
6x2 - 47x + 35 = 0
Factoring the quadratic equation gives (x - 7)(6x - 5) = 0. Since x must be greater than 2 (as 'A' takes x - 2 hours), the only valid solution is x = 7. Therefore, 'B' takes 7 hours to complete the work alone.
SIMILAR QUESTIONS
Suppose, 'A' can complete a job in 10 days, and 'A' and 'B' together can complete the same job in 6 days. In how many days can 'B' alone complete the job ?
Suppose A and B can complete a work together in 10 days. If B alone can complete the work in 15 days, then in how many days can A alone finish the work?
A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?
A, B and C alone can finish a job in 20, 25 and 30 days, respectively. A and B together start doing the job. However, they leave it after 10 days. The remaining part of the job is finished by C alone. How many days did C take to finish the job ?