A river flows from north to south at a speed of 10 km/h relative to the bank. A motorboat has a speed of 30
km/h in still water. A fisherman motors north for 2 h, and then, motors south back to his starting point. How
long did the return trip take?
distance = speed * time, so
2(30-10) = t(30+10)
t = 1
Well, that fisherman must have been in quite a hurry to get back to his starting point! But let's break it down. The river is flowing at 10 km/h and the motorboat can go 30 km/h in still water. When the fisherman motors north for 2 hours, he's going against the flow of the river, so the effective speed is 30 km/h - 10 km/h = 20 km/h. So in those 2 hours, he covers 20 km/h * 2 hours = 40 km.
Now, when he turns around and motors south, he'll have the current helping him. So the effective speed is 30 km/h + 10 km/h = 40 km/h. And since he needs to cover the same distance as before (40 km), the return trip will take 40 km / 40 km/h = 1 hour.
So, the return trip took 1 hour. But hey, at least the fisherman got a little help from the river current on his way back!
To solve this problem, we need to consider the relative velocities of the river and the boat.
We're given that the river flows from north to south at a speed of 10 km/h relative to the bank. This means that the boat's velocity relative to the ground when moving downstream (south) will be the sum of its velocity in still water and the velocity of the river. Similarly, the boat's velocity relative to the ground when moving upstream (north) will be the difference between its velocity in still water and the velocity of the river.
Let's break down the problem step-by-step:
1. Speed downstream (south):
- Boat's velocity in still water: 30 km/h
- Velocity of the river: 10 km/h
- Velocity downstream: 30 km/h + 10 km/h = 40 km/h
2. Speed upstream (north):
- Boat's velocity in still water: 30 km/h
- Velocity of the river: 10 km/h
- Velocity upstream: 30 km/h - 10 km/h = 20 km/h
3. Time taken to travel north for 2 hours:
- Velocity northward: 20 km/h
- Distance traveled north: Velocity northward * Time = 20 km/h * 2 h = 40 km
4. Time taken to travel back to the starting point:
- Velocity downstream: 40 km/h
- Distance traveled downstream: Velocity downstream * Time = 40 km/h * Time
Since the fisherman traveled 40 km north and then back to the starting point, the total distance is 80 km. The time taken for the return trip can be calculated using the formula: Distance = Velocity * Time.
80 km = 40 km/h * Time
Time = 80 km / 40 km/h
Time = 2 hours
Therefore, the return trip took 2 hours.
To find out how long the return trip took, we need to calculate the time it takes for the fisherman to travel south.
Let's break down the problem into different components:
1. The river is flowing from north to south at a speed of 10 km/h relative to the bank.
2. The motorboat has a speed of 30 km/h in still water.
3. The fisherman motorboats north for 2 hours.
First, let's find out the fisherman's effective speed when going north.
Since the river flows from north to south at 10 km/h and the motorboat has a speed of 30 km/h in still water, the fisherman's effective speed when going north will be the sum of their speeds: 30 km/h + 10 km/h = 40 km/h.
Now, let's calculate the distance the fisherman traveled when going north. We can use the formula: distance = speed * time.
Distance = 40 km/h * 2 h = 80 km
Now, we know that the fisherman traveled 80 km north. To return to his starting point, he needs to travel the same distance south.
To calculate the time it takes for the return trip, we can use the formula: time = distance / speed.
Time = 80 km / 30 km/h = 2.67 hours (approximately)
Therefore, the return trip took approximately 2.67 hours.