A river has a steady speed of 0.500 m/s.A student swims upstream a distane of 1.00 km and swims back to the starting point. If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? How much time is required in still water for the same length swim? How muh time is required in still water for the same length swim?.

Well, well, well, it seems like we have a swimming dilemma here. Let's dive in!

First, let's tackle the trip upstream. We need to figure out the time it takes to cover a distance of 1.00 km against the current. The river's speed is 0.500 m/s, so we need to subtract that from the student's swimming speed to get their effective speed.

1.20 m/s (student's speed) - 0.500 m/s (river's speed) = 0.700 m/s (effective speed)

To find the time it takes to swim upstream, we divide the distance by the effective speed:

Time = Distance / Speed
Time = 1.00 km / 0.700 m/s

Converting kilometers to meters:

Time = 1000 m / 0.700 m/s

Calculating it:

Time = 1428.57 seconds

Next, for the downstream trip, the river's speed will be helping our student. So, we add the river's speed to the student's swimming speed:

1.20 m/s (student's speed) + 0.500 m/s (river's speed) = 1.700 m/s (effective speed)

The distance is still the same, so we can use the same formula:

Time = Distance / Speed
Time = 1.00 km / 1.700 m/s

Converting kilometers to meters:

Time = 1000 m / 1.700 m/s

Calculating it:

Time = 588.24 seconds

Now, to find the total time for the whole trip, we add the time spent swimming upstream and the time spent swimming downstream:

Total time = Time upstream + Time downstream
Total time = 1428.57 seconds + 588.24 seconds

Calculating it:

Total time = 2016.81 seconds

Phew, that's quite a swim!

Now, let's talk about the time it would take in still water for the same length swim. Since the river wouldn't be interfering, the student's speed in still water would be their maximum speed, which is 1.20 m/s.

To find the time in still water, we use the same formula:

Time = Distance / Speed
Time = 1.00 km / 1.20 m/s

Converting kilometers to meters:

Time = 1000 m / 1.20 m/s

Calculating it:

Time = 833.33 seconds

So, there you have it! The total time for the trip with the river's current is 2016.81 seconds, while in still water, it would take 833.33 seconds.

Remember to pack some snacks for the journey, and maybe a clownfish friend to add some fun to the swim!

To find the time it takes for the trip, we need to calculate the time it takes for the upstream and downstream swims separately.

First, let's calculate the time it takes for the upstream swim.
The student is swimming against the current, which reduces their effective speed. We can find this reduced speed by subtracting the river's speed from the student's swimming speed: 1.20 m/s - 0.500 m/s = 0.70 m/s.

Next, we can find the time it takes for the upstream swim by dividing the distance by the reduced speed: 1.00 km / 0.70 m/s = 1428.57 seconds.

Now, let's calculate the time it takes for the downstream swim.
The student is swimming with the current, which increases their effective speed. We can find this increased speed by adding the river's speed to the student's swimming speed: 1.20 m/s + 0.500 m/s = 1.70 m/s.

We can find the time it takes for the downstream swim by dividing the distance by the increased speed: 1.00 km / 1.70 m/s = 588.24 seconds.

To find the total time for the trip, we add the upstream and downstream times: 1428.57 seconds + 588.24 seconds = 2016.81 seconds.

Therefore, the trip takes approximately 2016.81 seconds.

For the same length swim in still water, we can calculate the time required by dividing the distance by the student's swimming speed in still water: 1.00 km / 1.20 m/s = 833.33 seconds (approximately).

Therefore, in still water, it would take approximately 833.33 seconds for the same length swim.

To find the time it takes for the student to swim upstream and back downstream, we need to consider the speed of the river and the speed of the student in still water.

Let's first calculate the time it takes for the student to swim upstream for a distance of 1.00 km.

The speed of the river is 0.500 m/s, and the speed of the student in still water is 1.20 m/s. When swimming upstream, the speed of the student relative to the river will be the difference between their speeds:

Relative speed upstream = Speed in still water - Speed of the river
= 1.20 m/s - 0.500 m/s
= 0.70 m/s

Now we can calculate the time it takes for the student to swim upstream using the formula:

Time = Distance / Speed

Distance upstream = 1.00 km = 1000 m
Speed upstream = Relative speed upstream = 0.70 m/s

Time upstream = Distance upstream / Speed upstream
= 1000 m / 0.70 m/s
= 1428.57 seconds (rounded to two decimal places)

Next, we need to calculate the time it takes for the student to swim downstream for the same distance of 1.00 km.

When swimming downstream, the speed of the student relative to the river will be the sum of their speeds:

Relative speed downstream = Speed in still water + Speed of the river
= 1.20 m/s + 0.500 m/s
= 1.70 m/s

Similarly, we can use the formula Time = Distance / Speed:

Distance downstream = 1.00 km = 1000 m
Speed downstream = Relative speed downstream = 1.70 m/s

Time downstream = Distance downstream / Speed downstream
= 1000 m / 1.70 m/s
= 588.24 seconds (rounded to two decimal places)

Finally, to find the total time for the trip (upstream + downstream), we just need to add the times together:

Total time = Time upstream + Time downstream
= 1428.57 seconds + 588.24 seconds
= 2016.81 seconds (rounded to two decimal places)

Therefore, the total time for the trip (upstream and downstream) is approximately 2016.81 seconds.

To find the time required in still water for the same length swim, we can use the formula:

Time = Distance / Speed

Distance = 1.00 km = 1000 m
Speed in still water = 1.20 m/s

Time in still water = Distance / Speed
= 1000 m / 1.20 m/s
= 833.33 seconds (rounded to two decimal places)

Therefore, the time required in still water for the same length swim is approximately 833.33 seconds.

speed up = 1.2 - .5 = .7

speed down = 1.2 + .5 = 1.7

time up = 1000/.7 seconds
time down = 1000/1.7 seconds

add those times

in still water 2000/1.2 seconds