Rita’s boat has a top speed of 12 miles per hour in still water. While traveling on a river at top speed, she went 20 miles upstream in the same amount of time she went 40 miles downstream. Find the rate of the river current.
time=distance/velocity
upstream=time dowstream
time=20/(12-c)=40/(12+c)
24-2c=12+c
12=3c
c=4mi/hr
post it.
To solve this problem, we need to understand the concept of relative speed.
Let's assume the rate of the river current is "x" miles per hour.
When Rita goes downstream, her effective speed is increased by the current's speed. So, her speed downstream would be the sum of her boat's speed and the river current's speed, which is (12 + x) miles per hour.
When going upstream, the river current acts against the boat's speed, so her effective speed is decreased. Therefore, her speed upstream would be the difference between her boat's speed and the river current's speed, which is (12 - x) miles per hour.
Now, let's calculate the time it takes for Rita to travel each distance.
Time taken to go upstream = Distance / Speed upstream
Time taken to go downstream = Distance / Speed downstream
According to the problem, the time taken to go upstream is the same as the time taken to go downstream.
So, we can write the equation as:
20 / (12 - x) = 40 / (12 + x)
To solve this equation, we can cross multiply:
20(12 + x) = 40(12 - x)
240 + 20x = 480 - 40x
Combining like terms:
60x = 240
Simplifying:
x = 240 / 60
x = 4
Therefore, the rate of the river current is 4 miles per hour.