Tom and Jerry working separately can finish a work in 60 and 45 days respectively. They begin the work together and after 15 days, Jerry goes away. In how many days will the work be completed by Tom alone?
Question
Tom and Jerry working separately can finish a work in 60 and 45 days respectively. They begin the work together and after 15 days, Jerry goes away. In how many days will the work be completed by Tom alone?
Solution
Sure, let's solve this step by step:
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First, we need to find out how much work Tom and Jerry can do in a day. Tom can finish the work in 60 days, so he can do 1/60 of the work in a day. Similarly, Jerry can do 1/45 of the work in a day.
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When they work together, they can do (1/60 + 1/45) of the work in a day. This equals to 7/180 or 0.0389 of the work in a day.
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They work together for 15 days, so they can do 15 * 0.0389 = 0.5835 or 58.35% of the work in 15 days.
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After 15 days, Jerry goes away. So, the remaining work (1 - 0.5835) = 0.4165 or 41.65% needs to be done by Tom alone.
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As Tom can do 1/60 or 0.0167 of the work in a day, he will need 0.4165 / 0.0167 = 24.95 or approximately 25 days to finish the remaining work.
So, the total time to finish the work is 15 (days they worked together) + 25 (days Tom worked alone) = 40 days.
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