Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at speeds of v1 = 3.85 m/s and v2 = 5.66 m/s. Let s be the speed of the boats relative to the river and let v be the speed of the water relative to the shore (Earth).

Write an expression for the speed v of the the river relative to the shore using terms from the problem statement.
v =

Since v = speed of water relative to the shore, s = speed of boats relative to the river, v₁ = speed of first boat relative to the shore = 3.85 m/s and v₂ = speed of second boat relative to the shore = 5.66 m/s.

Since both boats are moving in opposite direction s relative to the river, their speeds relative to the shore are

v₁ = v + s (1) and v₂ = v - s (2)

To find the speed of the river relative to the shore v, we add (1) and (2),

So, v₁ = v + s (1)

+ v₂ = v - s (2)

v₁ + v₂ = 2v

v = (v₁ + v₂)/2

Substituting the values of the variables into the equation, we have

v = (3.85 m/s + 5.66 m/s)/2

v = 9.51 m/s/2

v = 4.755 m/s

v ≅ 4.76 m/s

So, the expression for the speed v of the the river relative to the shore is v = (v₁ + v₂)/2 and its value v = 4.76 m/s

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