36 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?
I know how they got 21 by adding 9 and tewnty ine but I don't know where the 45 camefrom,I know 9/15 + 12/15, but how did the 45 get in there?
To find the speed of the current, let's assume the speed of the current is 'x' mph.
When Junior is moving downstream, the speed of the boat is the sum of the speed in still water and the speed of the current: 15 + x mph.
Similarly, when Junior is moving upstream, the speed of the boat is the difference between the speed in still water and the speed of the current: 15 - x mph.
Now, let's calculate the time it takes for Junior to travel downstream and upstream:
Time taken downstream: distance / speed = 12 / (15 + x) hours
Time taken upstream: distance / speed = 9 / (15 - x) hours
According to the given information, the time taken downstream is equal to the time taken upstream:
12 / (15 + x) = 9 / (15 - x)
To solve this equation, we can cross-multiply:
12 * (15 - x) = 9 * (15 + x)
Now, let's simplify the equation:
180 - 12x = 135 + 9x
Combine the like terms:
-12x - 9x = 135 - 180
-21x = -45
Divide both sides by -21:
x = (-45) / (-21)
x ≈ 2.14
Therefore, the speed of the current is approximately 2.14 mph.