Explanation:
Let the speed of the current be c km/h.
When the ship sails with the current, its effective speed is (50 + c) km/h.
When the ship sails against the current, its effective speed is (50 - c) km/h.
We know that the distance traveled is the same in both cases, which is 60 km.
Let's use the formula:
time = distance / speed
When sailing with the current, the time taken is:
60 / (50 + c)
When sailing against the current, the time taken is:
60 / (50 - c)
We know that when sailing against the current, it takes 0.5 hours more time than when sailing with the current:
60 / (50 - c) = 60 / (50 + c) + 0.5
Simplifying the equation, we get:
60(50 + c) = 60(50 - c) + 0.5(50^2 - c^2)
3000 + 60c = 3000 - 60c + 1250 - 0.5c^2
Simplifying further,
120c = 1250 - 0.5c^2
0.5c^2 + 120c - 1250 = 0
Solving the quadratic equation by factoring or using the quadratic formula, we get:
c = 10 km/h (ignoring the negative root)
Therefore, the speed of the current is 10 km/h.