Answer:
Example 3. Same time problem: Upstream-Downstream.
First, let us explain the meaning of "upstream" and "downstream."
When a boat travels in the same direction as the current, we say that it is traveling downstream.
downstream
Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is
Downstream speed = b + c
When a boat travels against the current, it travels upstream.
upstream
In this case, its total speed is
Upstream speed = b − c
Problem. The speed of a boat in still water is 30 mph. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. Find the speed of the current.
Solution. The key to this type of problem is same time. That will give the equation,
Time upstream = Time downstream
Now, speed, or velocity, is distance divided by time -- so many miles per hour:
v = d
t
Therefore,
t = d
v
The equation will be
Time upstream = Time downstream
Distance upstream
Speed upstream = Distance downstream
Speed downstream
Let x be the speed of the current. Then according to the problem:
_5_
30 − x = 10
30 + x
Therefore,
5(30 + x) = 10(30 − x)
150 + 5x = 300 − 10x
5x + 10x = 300 − 150
15x = 150
x = 10 mph
Step-by-step explanation:
