Water leaks out of a 3,200-gallon storage tank (initially full) at the rate v '(t) = 80 -t, where t is measured in hours and v in gallons. a. how much water leaked out between 10 and 20 hours? b. how long will it take the tank to drain completely?

water leak is 650 gallons

time required to full drain is 80 hrs

Explanation:

given data

volume V = 3200 gallon

rate = V(t) = 80 - t

to find out

how much water leak between 10 and 20 hour and  drain complete

solution

we know here rate is 80 - t

so here rate will be

= 80 - t

and for time 10 and 20 hour

take integrate between 10 and 20

so water leak =   .....................1

water leak = ( 80t -

water leak = 650

so water leak is 650 gallons

and

we know here for full tank drain condition

water leak full = 80 t -

3200  = 80 t -

6400 = t² - 160 t

t = 80

so time required to full drain is 80 hrs

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