Find the number of days for John to complete the work alone in the following case:For doing some work, John takes 10 days more than Lee. If they...

It is given that for doing some work John takes 10 days
more than Lee. If both work together the work will complete in 12
days.

Let the rate at which John completes the work be J
and the rate at which Lee completes the work be L

We know
that J + L = 1/12

1/L - 1/J =
10

=> L - J = 10
L*J

Substitute L = 1/12 -
J

=> 1/12 - J - J = 10*(1/12 -
J)*J

=> (1 - 24J)/12 = 10J/12 -
120J^2/12

=> 1 - 24J = 10J -
120J^2

=> 120J^2 - 34J + 1 =
0

=> 120J^2 - 30J - 4J + 1 =
0

=> 30*J(4J - 1) - 1(4J - 1) =
0

=> (30J - 1)(4J - 1) =
0

=> J = 1/30 or J =
1/4

The rate at which John works is
1/30

The number of days taken by John alone
to finish the work is 30.