math

A water reservoir has two inlets and one outlet. Through the inlet it can be filled in 3 hours and 3 hours 45 minutes respectively. It can be emptied completely in 1 hour by the outlet. If the two inlets are opened at 01:00 pm and 02:00 pm respectively and the outlet at 03:00 pm then it will be emptied at.
(a) 05 : 55 pm (b) 05 : 00 pm (c) 05 : 20 pm (d) 05 : 30 pm (e) none of these

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  1. let the volume of the reservoir be w units

    let the total time from noon to empty time be t:00 hrs

    rate of first inlet = w/3
    rate of 2nd inlet = w/3.75
    rate of outlet = w/1

    time outlet is open = t-3
    time 2nd inlet open = t-2
    time 1st inlet is open = t -1

    (w/3)(t-1) + (w/3.75)(t-2) - w(t-3) = 0 <--- it is empty
    divide by w
    (t-1)/3 + (t-2)/3.75 - t + 3 = 0
    multiply by 11.25
    3.75(t-1) + 3(t-2) - 11.25t + 33.75 = 0

    t = 16/3 or 5 1/3 hrs, which would put it at 5:20 pm

    I will let you check my work

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