Given:
Upstream distance = 12 km, Downstream distance = 20 km
Time taken = 4 hours
Upstream distance = 18 km, Downstream distance = 10 km
Time taken = 4 hours
Formula used:
Speed in still water (S) and speed of stream (R) are given by:
Upstream speed = S - R
Downstream speed = S + R
Time = Distance / Speed
Calculation:
Using time equation for first case:
⇒ \(\dfrac{12}{S - R} + \dfrac{20}{S + R} = 4 \)
Using time equation for second case:
⇒ \(\dfrac{18}{S - R} + \dfrac{10}{S + R} = 4 \)
Let \(x = \dfrac{1}{S - R} \) and \(y = \dfrac{1}{S + R}\), then:
⇒ \(12x + 20y = 4 \)
⇒ \(18x + 10y = 4 \)
Multiplying first equation by 3 and second by 2:
⇒ \(36x + 60y = 12 \)
⇒ \(36x + 20y = 8 \)
Subtracting:
⇒ \(40y = 4 \) ⇒ \(y = \dfrac{1}{10}\)
Substituting in first equation:
⇒ \(12x + 20 \times \dfrac{1}{10} = 4 \)
⇒ \(12x + 2 = 4 \) ⇒ \(x = \dfrac{1}{6}\)
Since \(x = \dfrac{1}{S - R}\) and \(y = \dfrac{1}{S + R}\):
⇒ \(S - R = 6 \) and \(S + R = 10\)
Adding equations:
⇒ \(2S = 16 \) ⇒ \(S = 8 \)
∴ The speed in still water is 8 km/h.