Math word problem.

Question

For a certain bathtub, the cold water faucet can fill the tub in
12

minutes. The hot water faucet can fill the tub in
13

minutes. If both faucets are used together, how long will it take to fill the tub?

Do not do any rounding.

Answer 1

Think of it this way ... the cold faucet can fill 1/12 of the tub in one minute, and the hot faucet can fill 1/13 of the tub in one minute.  Adding 1/12 and 1/13 will tell us what fraction of the tub will be filled in one minute if both faucets are open.  The reciprocal of this number will be the number of minutes needed to fill the tub if both faucets are open.

1/12 + 1/13 = 13/156 + 12/156 = 25/156.  The reciprocal of 25/156 is 156/25 or 6.24 , which is the total time (in minutes) required if both faucets are open.

Check:  Two cold faucets would fill the tub in 6 minutes, and two hot faucets will fill the tub in 6.5 minutes.  So a value between those two numbers is logical.