The swim portion of a triathlon takes place in a river and is an out-and-back course. The river has a steady current that is 0.400 m/s and the athletes swim against the current for 750m before returning and swimming with the current for the second 750m. If one competitor can swim at a steady speed of 1.10 m/s in still water, how long will it take to swim the river? How long without a current?

To find out how long it will take to swim the river, we need to calculate the total time for each leg of the swim and add them together.

First, let's find the time it takes to swim against the current for 750m. We can use the formula: time = distance / speed. Given that the current is against the swimmer, the effective speed is the swimmer's speed in still water minus the current speed. So the effective speed is 1.10 m/s - 0.400 m/s = 0.700 m/s.

The time to swim against the current is then: time_1 = 750m / 0.700 m/s.

Next, let's find the time it takes to swim with the current for the second 750m. Since the current is now helping the swimmer, the effective speed is the swimmer's speed in still water plus the current speed. So the effective speed is 1.10 m/s + 0.400 m/s = 1.500 m/s.

The time to swim with the current is: time_2 = 750m / 1.500 m/s.

Finally, we can find the total time to swim the river by adding the times for each leg: total_time = time_1 + time_2.

To calculate how long it would take to swim the river without any current, we just need to divide the total distance (1500m) by the swimmer's speed in still water (1.10 m/s).

Let's perform the calculations:

time_1 = 750m / 0.700 m/s = 1071.4 seconds
time_2 = 750m / 1.500 m/s = 500.0 seconds

total_time = time_1 + time_2 = 1071.4 seconds + 500.0 seconds = 1571.4 seconds

time_without_current = 1500m / 1.10 m/s = 1363.6 seconds

Therefore, it would take approximately 1571.4 seconds (or 26 minutes and 11.4 seconds) to swim the river with the current, and 1363.6 seconds (or 22 minutes and 43.6 seconds) to swim the river without any current.

To determine the time it takes to swim the river, we need to consider both the time spent swimming against the current and the time spent swimming with the current.

First, let's calculate the time spent swimming against the current. The distance is 750 meters, and the current is 0.400 m/s against the swimmer. So the effective speed of the swimmer against the current is:

effective speed = swimmer's speed - current speed
= 1.10 m/s - 0.400 m/s
= 0.70 m/s

Now we can calculate the time spent swimming against the current:

time against current = distance / effective speed
= 750m / 0.70 m/s
= 1071.43 seconds (rounded to two decimal places)
≈ 1071 seconds

Next, let's calculate the time spent swimming with the current. The distance is again 750 meters, but this time the current helps the swimmer. So the effective speed of the swimmer with the current is:

effective speed = swimmer's speed + current speed
= 1.10 m/s + 0.400 m/s
= 1.50 m/s

Now we can calculate the time spent swimming with the current:

time with current = distance / effective speed
= 750m / 1.50 m/s
= 500 seconds

Finally, to get the total time it takes to swim the river, we add the times spent against and with the current:

total time = time against current + time with current
= 1071 seconds + 500 seconds
= 1571 seconds

So, it will take approximately 1571 seconds to swim the river with the current. Without a current, the swimmer's speed in still water would be the same, so it would take the same amount of time. Thus, the time to swim without a current would also be 1571 seconds.