F.4 MATHS

Let V =r(m+t), where r is a constant (1)
and m = s(t+V), where s is another constant (2)

subsitute (2) into (1)
V = r [s(t+V) + t]
V = r [(s+1)t + sV]
V = r (s+1)t + rsV
(1-rs)V = r(s+1)t
V = [r(s+1) / (1-rs)] t, where [r(s+1) / (1-rs)] is a constant (3)

subsitute (3) into (2)
m = st + sV
m = st + s[r(s+1) / (1-rs)] t
m = s {1 + [r(s+1) / (1-rs)] } t
m = s { [(1-rs) + r(s+1)] / (1-rs) } t
m = s { [1-rs+rs+r] / (1-rs) } t
m = [s(r+1) / (1-rs)] t, where [s(r+1) / (1-rs)] is also a constant

therefore V varies directly as t,
and m also varies directly as t

a) V =k(m+t)
V=km+kt
kt=V-km
t=(V-km)/k

b) m=k(t+V)
m=kt+kV
kt=m-kV
t=(m-kV)/k