#### Answer

$12.7$ minutes

#### Work Step by Step

Let both david and allie work together in $T$ minutes
(Fraction work done in a minute by david)+ (Fraction work done in a minute by allie)T=1
$\implies (\dfrac{1}{20}+\dfrac{1}{35})T=1$
$\implies (\dfrac{35+20}{700})T=1$
$T=\frac{700}{55}$
or, $T=12.7$ minutes