Answer:
(A) 6 minutes
Explanation:
it takes 20 and 30 minutes to fill the whole tub, so it takes only 10 and 15 minutes to fill half the tub.
in 1 minute the cold faucet can do 1/10 of the work (to fill half the tub).
in 1 minute the hot faucet can do 1/15 of the work (to fill half the tub).
so, together, they do in 1 minute
1/10 + 1/15 of the work (to fill half the tub).
1/10 + 1/15 =3/30 + 2/30 = 5/30 = 1/6
so, together, they do in 1 minute 1/6 of the work (to fill half the tub).
therefore, for the full work they need 6 times that amount of time of 1 minute.
together, they can fill half the tub in 6 minutes.