Manuel has a boat that can move at a speed of 30 kn/h in still water. He rides 280 km downstream in a river in the same time it takes to ride 70 km upstream. What is the speed of the river?
8u=3u+35
You are solving equations with Variables on Both Sides.
Let R = speed of river
Distance = rate * time
Therefore time = Distance/rate
280/(30+R) = 70/(30-R)
Solve for R.
To solve this problem, we need to use the concept of relative velocity. Let's assume the speed of the river is 'x' km/h. When Manuel is traveling downstream, his effective speed will be the sum of his boat's speed and the speed of the river, which will be (30 + x) km/h. When he travels upstream, his effective speed will be the difference between his boat's speed and the speed of the river, which will be (30 - x) km/h.
Now, let's calculate the time it takes for Manuel to travel downstream and upstream.
When Manuel rides 280 km downstream, the time taken can be calculated using the formula:
Time = Distance / Speed
Time downstream = 280 km / (30 + x) km/h
Similarly, when Manuel rides 70 km upstream, the time taken can be calculated using the same formula:
Time = Distance / Speed
Time upstream = 70 km / (30 - x) km/h
According to the problem, these two times are equal, which gives us the equation:
280 / (30 + x) = 70 / (30 - x)
To solve this equation, we cross-multiply:
280(30 - x) = 70(30 + x)
Simplifying further:
8400 - 280x = 2100 + 70x
Combining like terms:
350x = 6300
Dividing both sides by 350:
x = 18
Therefore, the speed of the river is 18 km/h.