To solve for the average speed of Tatjana Schoenmaker in swimming across the pool and then returning to the starting point, let's break down the problem step-by-step:
1. Determine the time for one length of the pool:
- Tatjana takes 23.2 seconds to swim one length of the pool.
2. Determine the extra time to return:
- Returning to the starting point takes her 1.7 seconds more than the time taken for one length.
- To find the return time:
[tex]\[
\text{Return time} = 23.2 \; \text{seconds} + 1.7 \; \text{seconds} = 24.9 \; \text{seconds}
\][/tex]
3. Calculate the total time to complete the event:
- Total time includes the time for one length plus the return time.
[tex]\[
\text{Total time} = 23.2 \; \text{seconds} + 24.9 \; \text{seconds} = 48.1 \; \text{seconds}
\][/tex]
4. Calculate the total distance swum:
- Tatjana swims two lengths of the pool (one length to the end and one length back to the starting point).
[tex]\[
\text{Total distance} = 2 \; \text{lengths}
\][/tex]
5. Calculate the average speed:
- Speed is given by the formula:
[tex]\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\][/tex]
- Here, the total distance is 2 lengths of the pool, and the total time is 48.1 seconds. So, the average speed is:
[tex]\[
\text{Average speed} = \frac{2 \; \text{lengths}}{48.1 \; \text{seconds}} \approx 0.04158 \; \text{lengths per second}
\][/tex]
Therefore, Tatjana's average speed to complete the event is approximately [tex]\( 0.04158 \)[/tex] lengths per second.
