Yefim S. answered • 07/06/20

Math Tutor with Experience

Let m is m of solt at time t, then dm/dt = - 3m/(v_{0} + 4t), At t = 0 m = m_{0} and v_{0} + 4t = v. We separate variables:

dm/m = - -3dt/(v_{0} + 4t). So, lnm = - 3/4 ln(v_{0} + 4t) + lnC, m = C(v_{0} + 4t)^{- 3/4}. m_{0} = Cv_{0}^{-3/4}.

Now 120 = 40 + 4t, so t = 20 min. m = C(120)^{-3/4} = 11, C = 11·120^{3/4} = 398.82

For mass of solt we have now m = 398.82·(v_{0} + 4t)^{-3/4}. If t = 0 m_{0} = 398.82·v_{0}^{-3/4 }= 398.82/40^{3/4} = 25.87 kg .