Two men $A$ and $B$ can together complete a task in $12$ days. If $B$ alone completes the same task, he takes $10$ days more than $A.$ How many days does it take for $B$ alone to complete the entire task?
2026-03-27 12:03:03.1774612983
Word Problem Involving Completing Tasks in Different Amounts of Time
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A performs a tasks/day.
B performs b tasks/day.
A performs 1 task in 1/a days.
B performs 1 task in 1/b days.
1/b = 1/a + 10 days.
A and B perform a + b tasks/day.
A and B perform 1 task in 1/(a + b) days.
1/(a + b) = 12 days.
Justify those steps,
solve those two equations for a and b,
and thusly deduce the answer.