A cold-water faucet can fill a sink in 1212 min, and a hot-water faucet can fill it in 1515 min. the drain can empty the sink in 2525 min. if both faucets are on and the drain is open, how long will it take to fill the sink?

9.1 minutes.

Step-by-step explanation:

Let t represent time taken to fill the tank.

We have been given that a cold water faucet can fill a sink in 12 min, so the part of sink filed in 1 minute would be .

The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be .

The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be .

The part of 1 full tank filled in t minutes, when both faucets are on and the drain is open would be:

Make a common denominator:

Therefore, it will take 9.1 minutes to fill the sink.

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.