To solve this problem, let us assume linear motion so that we can use the equation:
t = d / v
where t is time, d is distance and v is velocity
First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:
35 / Vu + 55 / Vd = 12 ---> 1
30 / Vu + 44 / Vd = 10 ---> 2
We rewrite equation 1 in terms of Vu:
(35 / Vu + 55 / Vd = 12) Vu
35 + 55 Vu / Vd = 12 Vu
12 Vu – 55 Vu / Vd = 35
Vu (12 – 55 / Vd) = 35
Vu = 35 / (12 – 55 / Vd) ---> 3
Also rewriting equation 2 to in terms of Vu:
Vu = 30 / (10 – 44 / Vd) ---> 4
Equating 3 and 4:
35 / (12 – 55 / Vd) = 30 / (10 – 44 / Vd)
35 (10 – 44 / Vd) = 30 (12 – 55 / Vd)
Multiply both sides by Vd:
350 Vd – 1540 = 360 Vd – 1650
10 Vd = 110
Vd = 11 km / h
Using equation 3 to solve for Vu:
Vu = 35 / (12 – 55 / 11)
Vu = 5 km / h
Answers:
Vu = 5 km / h = velocity upstream
Vd = 11 km / h = velocity downstream
