A bucket is leaking water linearly over time If the bucket h

A bucket is leaking water linearly over time. If the bucket had 14 gallons at 10: 30 am and 6 gallons at 3: 00 pm the same day, at approximately what time will the bucket be completely empty?

Solution

Let 10:30am be the starting time. so bucket had 14 gallons at the start

Let equation be

y = mt+14

At 3: am bucket had 6 gallons. so after 4.5 hours, bucket had 6 gallons

6 =m*4.5+14

m = -16/9

So equation is y = -16/9t+14

put y =0 and solve for t

t = 63/8 or 7.875

So, after 7 hours and 52.5 minutes , bucket will be emptry

That is at 6: 22.5 PM bucket will be empty