a man was trying to swim to a buoy placed at a distance of 200m out in the sea. it took him 1 min to swim 20m. then a wave pushed him back 10m and he rested for about 1min before swimming again. he continued in his way for the rest of their journey. how long would it take the man to swim to the buoy?

Make a stepped graph.

*At the end of 1 min he is at 20 m
at the beginning of 2 min he is at 10 ,
at the end of 2 min he is at 10 m , (he rested 1 min)
*at the end of 3 min he is at 30 m
at the beginning of 4 min he is at 20m
at the end of 4 min he is at 20 m
* at the end of 5 m he is at 40 m

look at the lines with a *
..
we have (1,20) , (3,30) , (5,40)
slope = 10/2 = 5
distance = 5(minute) + b , using (1,20)
20 = 5(1) + b
15 = b

distance = 5(minute) + 15 , where minute is an integer

200 = 5m+15
5m = 185
m = 37
He will reach the 200 m mark at the end of the 37th minute.

We will assume that as soon as he reaches the 200 m mark, he will grab and hold on before the wave pushes him back.

Let's break down the steps the man takes and calculate the total time it would take him to swim to the buoy.

Step 1: The man swims 20m in 1 minute.
Step 2: The man is pushed back 10m by a wave, bringing him back to 10m from the starting point.
Step 3: The man rests for about 1 minute.
Step 4: The man starts swimming again.

To calculate the total time, we need to determine how many times the man goes through this cycle of swimming, being pushed back, and resting until he reaches the buoy.

Each cycle covers a distance of 20m (swim) - 10m (pushed back) = 10m.

So, the number of cycles the man needs to go through to cover a distance of 200m is 200m / 10m = 20 cycles.

In each cycle, the man takes 1 minute to swim and 1 minute to rest, so each cycle takes 1 minute (swimming) + 1 minute (resting) = 2 minutes.

To find the total time, we multiply the number of cycles by the time per cycle: 20 cycles * 2 minutes per cycle = 40 minutes.

Therefore, it would take the man 40 minutes to swim to the buoy.

To find the total time it would take for the man to swim to the buoy, we need to break down the different segments of his journey and add up the times.

First, let's calculate the time it took him to swim the initial 20m:
Time = Distance / Speed
Time = 20m / (20m/min)
Time = 1 min

Next, we need to account for the wave that pushed him back 10m. Since he rested for about 1 min before swimming again, we can consider this as a separate segment. The wave pushed him back, but we need to calculate the overall distance he swam during the first segment:
Total distance swam = Distance swam forward - Distance pushed back
Total distance swam = 20m - 10m
Total distance swam = 10m

Now, let's calculate the time it took him to swim the remaining distance of 180m:
Time = Distance / Speed
Time = 180m / (20m/min)
Time = 9 min

Adding up the times for each segment:
Total time = Time swam initially + Time swam after being pushed back
Total time = 1 min + 9 min
Total time = 10 min

Therefore, it would take the man a total of 10 minutes to swim to the buoy.

i think it will take 40 min