A tourist traveled on a motorboat against the current for 25 km. And then returned back on a raft. In the boat the tourist traveled for 10 hours less than on the raft. Find the speed of the current if the speed of the motorboat in still water is 12 km/hour.
To solve this problem, let's assume that the speed of the current is "c" km/hour.
When the tourist is traveling against the current, their effective speed is reduced by the current's speed. Therefore, the speed of the boat against the current is (12 - c) km/hour.
Let's say the time it takes to travel 25 km against the current is "t" hours. According to the given statement, the time it takes to travel on the raft is "t + 10" hours.
Since speed = distance/time, we can set up the following equations based on the information provided:
25 = (12 - c) * t ... Eqn (1)
25 = (12 + c) * (t + 10) ... Eqn (2)
Now, let's solve these equations step-by-step:
From Eqn (1), we get:
t = 25 / (12 - c)
Substituting the value of t in Eqn (2), we get:
25 = (12 + c) * (25 / (12 - c) + 10)
Simplifying further:
25(12 - c) = (12 + c) * (25 + 10(12 - c))
300 - 25c = 12(25 + 12 - c)
300 - 25c = 12(37 - c)
300 - 25c = 444 - 12c
- 25c + 12c = 444 - 300
- 13c = 144
c = 144 / 13
c ≈ 11.08
Therefore, the speed of the current is approximately 11.08 km/hour.
To solve the problem, we need to find the speed of the current.
Let's assume the speed of the current is C km/hour.
When the tourist traveled on the motorboat against the current, the speed of the boat relative to the shore would be reduced. We calculate this by subtracting the speed of the current from the speed of the motorboat:
Speed of the boat against the current = Speed of the motorboat - Speed of the current
= 12 km/hour - C km/hour
= (12 - C) km/hour
Similarly, when the tourist traveled on the raft with the current, the speed of the boat relative to the shore would be increased:
Speed of the boat with the current = Speed of the motorboat + Speed of the current
= 12 km/hour + C km/hour
= (12 + C) km/hour
Using the formula: Speed = Distance / Time, we can find the time taken for each leg of the journey.
Time taken on the motorboat = Distance / Speed
= 25 km / (12 - C) km/hour
= (25 / (12 - C)) hours
Time taken on the raft = Distance / Speed
= 25 km / (12 + C) km/hour
= (25 / (12 + C)) hours
According to the problem, the time taken on the motorboat is 10 hours less than the time taken on the raft:
(25 / (12 - C)) = (25 / (12 + C)) - 10
To solve this equation for C, we can cross-multiply and simplify:
25(12 + C) = 25(12 - C) - 10(12 - C)
300 + 25C = 300 - 25C - 120 + 10C
300 + 25C = 300 - 25C + 10C - 120
25C + 25C - 10C = 300 - 120 - 300
40C = -120
Divide both sides of the equation by 40 to solve for C:
C = -120 / 40
C = -3
Since speed cannot be negative, we disregard the negative value. Therefore, the speed of the current is 3 km/hour.