a paddle boat can move at a speed of 14 km/h in still water. the boat is paddled 16 km downstream in a river in the same time it takes to go 8km upstream. what is the speed of the river?
evidently the downstream speed is twice as fast as the upstream speed. So,
14+x = 2(14-x)
To find the speed of the river, let's assume the speed of the river is "x" km/h.
When the boat moves downstream, it gets a boost from the current, so its effective speed is the sum of the boat speed and the speed of the river:
Effective speed downstream = (Boat speed) + (River speed) = 14 + x km/h
When the boat moves upstream, it has to work against the current, so its effective speed is the difference between the boat speed and the speed of the river:
Effective speed upstream = (Boat speed) - (River speed) = 14 - x km/h
We are given that it takes the same amount of time for the boat to paddle 16 km downstream as it takes to go 8 km upstream.
Distance downstream = 16 km
Distance upstream = 8 km
Time taken downstream = Time taken upstream
Distance/Speed = Time
16/(14 + x) = 8/(14 - x)
Now let's solve this equation step by step:
Cross multiplying the equation:
16 * (14 - x) = 8 * (14 + x)
224 - 16x = 112 + 8x
Rearranging the equation:
224 - 112 = 8x + 16x
112 = 24x
Dividing both sides by 24:
112/24 = x
4.67 = x
Therefore, the speed of the river is approximately 4.67 km/h.
To find the speed of the river, we need to set up an equation based on the given information.
Let's assume the speed of the river is represented by 'x' km/h.
When the boat is paddled downstream, the speed of the river helps in increasing the boat's speed. So the effective speed becomes (14 + x) km/h.
Similarly, when the boat is paddled upstream, the speed of the river opposes the boat's speed. So the effective speed becomes (14 - x) km/h.
We are given that the boat travels 16 km downstream in the same time it takes to go 8 km upstream. This means the time taken for both journeys is equal.
We can use the formula, Time = Distance / Speed, to set up the equation:
Time downstream = Time upstream
Distance downstream / Speed downstream = Distance upstream / Speed upstream
16 / (14 + x) = 8 / (14 - x)
Now, we can cross-multiply to get rid of the fractions:
16(14 - x) = 8(14 + x)
Simplifying this equation:
224 - 16x = 112 + 8x
Collect like terms:
-16x - 8x = 112 - 224
-24x = -112
Dividing both sides by -24:
x = -112 / -24
x = 4.6667 km/h
Therefore, the speed of the river is approximately 4.67 km/h.