5.) A boat makes a trip downstream in 5 hours. The return trip against the current takes 12 hours. If the speed of the current is 3 1/2 km/h, what is the speed of the boat in still water?
6.) How far does the boat referred to in Exercise 5 travel (one-way)?
since distance = speed * time,
(x+3.5)(5) = (x-3.5)(12)
x = 8.5
Now you can easily show how far it went.
To find the speed of the boat in still water, we can use the formula:
Speed of boat in still water = (Speed downstream + Speed upstream) / 2
Let's denote the speed of the boat in still water as "B" (in km/h).
1. Speed downstream:
We know that the boat takes 5 hours to travel downstream. During this time, the speed of the boat relative to the ground is the sum of the speed of the boat in still water (B) and the speed of the current (3 1/2 km/h). So, the speed downstream is (B + 3 1/2) km/h.
2. Speed upstream:
Similarly, the boat takes 12 hours to travel upstream. During this time, the speed of the boat relative to the ground is the difference between the speed of the boat in still water (B) and the speed of the current (3 1/2 km/h). So, the speed upstream is (B - 3 1/2) km/h.
Now, we can use these values to find the speed of the boat in still water.
Speed of boat in still water = (Speed downstream + Speed upstream) / 2
B = [(B + 3 1/2) + (B - 3 1/2)] / 2
B = (2B) / 2
B = B
So, the speed of the boat in still water is B km/h, which means the speed does not depend on the speed of the current. Hence, it is simply the average of the speeds downstream and upstream.
Now, let's find the distance traveled by the boat (one-way).
Distance = Speed x Time
Using the speed downstream (B + 3 1/2 km/h), we can find the distance traveled downstream by multiplying it by the time taken (5 hours):
Distance downstream = (B + 3 1/2) km/h * 5 hours
Similarly, using the speed upstream (B - 3 1/2 km/h), we can find the distance traveled upstream by multiplying it by the time taken (12 hours):
Distance upstream = (B - 3 1/2) km/h * 12 hours
However, the distances downstream and upstream are the same, as the boat travels the same distance in both directions. So, we can set them equal to each other:
(B + 3 1/2) km/h * 5 hours = (B - 3 1/2) km/h * 12 hours
Now, solve for B to find the speed of the boat in still water.