Question
A and B can finish a task together in '2t' days. B alone
can complete the task in 10 days, while A alone can do it in '5t' days. Find the value of 't'.Solution
ATQ,
Given: A and B together can do the work in 2t days B alone can do the work in 10 days A alone can do the work in 5t days Their work rates will be A’s rate = 1 / (5t), B’s rate = 1 / 10 and A + B’s rate = 1 / (2t) Set up the equation A’s rate + B’s rate = (A + B)'s rate So, (1 / 5t) + (1 / 10) = 1 / (2t) Multiply both sides by 10t to eliminate denominators 10t * (1 / 5t) + 10t * (1 / 10) = 10t * (1 / 2t) 2 + t = 5 t = 3
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