Question

A vat containing 10,000 gallons of black ink supplies 3 different printing presses. Press 1 uses 12 gallons per minute, press 2 uses 10 gallons per minute and press 3 uses 15 gallons per minute. If the vat was full at 7:30 AM and all three presses run constantly when will the vat run dry?

Answer 1

three presses use 37 gal per min. So they will use 10000 gal in 10000 / 37 = 270.27 min, or about 4 1/2 hrs. So counting from 7:30 am, the vat will run dry at 12 noon

Answer 2

If the vat was full at 7:30 AM, then vat will run dry after 12 PM.

Explanation:

Total ink in a vat = 10,000 gal

Ink used by press -1 = 12 gal/ min

Ink used by press-2 = 10 gal/min

Ink used by press-3 = 15 gal/min

Total ink used by vat per minute :

=12 gal/ min+10 gal/ min+15 gal/ min=37 gal /min

Duration for which vat will run until the vat runs dry= T

`T* 37 gal/min=10,000`

t = 270.2702 min = 4.5 hours (1 hr = 60 min)

4.5 hours = 4 hours 30 mins

Time in clock when nk in the vat was 10,000 gal = 7:30 AM

Time at which vat will run dry = 7:30 AM + 4 hour + 30 minutes =12 PM

If the vat was full at 7:30 AM, then vat will run dry after 12 PM.