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?

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-09-14T12:02:23+02:00

Answer:

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

[tex]\frac{dV(t)}{dt}[/tex] = 80 - t

and for time 10 and 20 hour

take integrate between 10 and 20

so water leak = [tex]\int\limits^ {20}_ {10} {(80-t)} \, dt[/tex] .....................1

water leak = ( 80t - [tex]\frac{t^{2} }{2} )^{20}_{10}[/tex]

water leak = 650

so water leak is 650 gallons

and

we know here for full tank drain condition

water leak full = 80 t - [tex]\frac{t^{2} }{2} [/tex]

3200 = 80 t - [tex]\frac{t^{2} }{2} [/tex]

6400 = t² - 160 t

t = 80

so time required to full drain is 80 hrs