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Upstream, downstream. Junior’s boat will go 15 miles per
hour in still water. If he can go 12 miles downstream in the
same amount of time as it takes to go 9 miles upstream,
then what is the speed of the current?
let the speed of the current be x mph
so the time taken to go 9 miles upstream (against the current) = 9/(15-x)
and the time taken to go 12 miles downstream (with the current) = 12/(15+x)
but we are told the times are the same, so
12/(15+x) = 9/(15-x)
cross-multiply
solve for x to get the speed (I got around 2.14)
To solve this problem, we can consider the concept of relative speed. Let's assume the speed of the current is represented by 'c' miles per hour.
When Junior is traveling downstream (in the same direction as the current), his effective speed will be the sum of the speed of the boat and the speed of the current. So, his effective speed will be (15 + c) miles per hour.
Similarly, when Junior is traveling upstream (against the current), his effective speed will be the difference between the speed of the boat and the speed of the current. So, his effective speed will be (15 - c) miles per hour.
Now, we are given that Junior can travel 12 miles downstream in the same amount of time it takes to go 9 miles upstream. We can use the formula: time = distance/speed to set up the equation.
For the downstream journey:
Time taken = Distance/Speed
12/(15 + c)
For the upstream journey:
Time taken = Distance/Speed
9/(15 - c)
Since the times are equal for both journeys, we can equate the two expressions:
12/(15 + c) = 9/(15 - c)
To solve this equation, we can cross multiply:
12(15 - c) = 9(15 + c)
180 - 12c = 135 + 9c
Next, we can simplify the equation by bringing the variables to one side:
-12c - 9c = 135 - 180
-21c = -45
Finally, solve for 'c' by dividing both sides of the equation by -21:
c = -45 / -21
c = 2.14 (approximately)
Therefore, the speed of the current is approximately 2.14 miles per hour.