Two diggers

There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster.

a) how long took to dig a pit second digger
b) how long took dig together

Correct result:

a =  23 h
b =  15.33 h

Solution:

$a = 46/2 = 23 \ \text{h}$
$b(\dfrac{1}{ 46} + \dfrac{1}{a}) = 1 \ \\ b = \dfrac{1}{ \dfrac{1}{ 46} + \dfrac{ 2}{ 46}} = 15.33 \ \text{h}$

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