Two boat landings are 3.0 km apart on the same bank of a stream that flows at 1.6 km/h. A motorboat makes the round trip between the two landings in 50 minutes. What is the speed of the boat relative to the water?
How do I factor in the fact that velocity is subtracted by 1.6 when I wasn't given velocity. );
50 min = .833 hr
t1 = 3/(1.6+v)
t2 = 3/(1.6-v)
.833 hr = t1 + t2
To solve this problem, we can use the concept of relative velocity. The speed of the boat relative to the water can be found by considering the speed of the boat and the speed of the stream.
Let's denote the speed of the boat as "V" and the speed of the stream as "S". We are given that the distance between the two boat landings is 3.0 km and that the stream flows at a speed of 1.6 km/h.
In the upstream direction (against the current), the effective speed of the boat will be reduced by the speed of the stream. In the downstream direction (with the current), the effective speed of the boat will be increased by the speed of the stream.
Now, let's analyze the round trip:
1. Upstream: The boat is moving against the current, so the effective speed will be (V - S) km/h.
The distance traveled upstream is 3.0 km.
2. Downstream: The boat is moving with the current, so the effective speed will be (V + S) km/h.
The distance traveled downstream is also 3.0 km.
We are given that the round trip between the two landings takes 50 minutes. It means that the total time spent upstream and downstream is 50 minutes.
Using the formula:
time = distance / speed
1. Upstream: time = 3.0 km / (V - S) km/h
2. Downstream: time = 3.0 km / (V + S) km/h
Since the total time upstream and downstream is given as 50 minutes, we can write the following equation:
3.0 km / (V - S) km/h + 3.0 km / (V + S) km/h = 50 minutes
To convert 50 minutes into hours, we divide by 60:
50 minutes / 60 = 0.833 hours
Now we have the equation:
3.0 km / (V - S) km/h + 3.0 km / (V + S) km/h = 0.833 hours
We can solve this equation to find the value of V, the speed of the boat relative to the water.