Christa, Jada, and Yvette were swimming laps at an outdoor swimming pool. Christa planned to swim for Cm minutes at a constant speed and swim a total of CL laps. Jada planned to swim for Jm minutes at a constant speed and swim a total of JL laps. Yvette planned to swim for Ym minutes at a constant speed and swim a total of YL laps. They started swimming at the same time and stopped swimming at the same time when lightning began to occur. If Christa lost 40% of her planned swimming time, which of the 3 swimmers lost the greatest percentage of her planned laps?Since the passage says that the three swimmers started swimming at the same time and stopped swimming at the same time, we know that they all swam for the same amount of time. So, to determine which of the 3 swimmers lost the greatest percentage of her planned laps, we need a way to determine the relative percentages of their swimming they would have completed in the same amount of time.
Key to notice is that the swimmers all swam at constant speeds. So, the percentage of their planned time that they swam is equal to the percentage of their planned laps that they swam. For example, a swimmer who swam at a constant rate for half her planned time would complete half her planned laps.
1) CL = 18, JL = 25, YL = 20This choice tells us only how many laps each planned to complete. That information does not enable us to connect their percentages completed with the amount of time they swam.
After all, they could have been swimming at the same speed or different speeds. So, even though this choice tells us that Jada and Yvette planned to complete more laps than Christa, we don't have enough information to determine what percentage of their laps they completed in the same amount of time.
For instance, if Jada and Yvette swam at the same speed as Christa, then Jada lost the greatest percentage of her planned laps since she had the most to complete and thus completed the smallest percentage of her laps in the same amount of time as the other two.
The exact numbers in that case are the following:
Christa: 40% of time lost means 40% of laps lost. 18 x .60 = 10.8 laps completed
Jada: 10.8 laps completed, (25 - 10.8)/25 = 14.2/25 = 56.8% lost
Yvette: 10.8 laps completed, (20 - 10.8)/20 = 9.2/20 = 46% lost
On the the other hand, if Jada and Yvette swam twice as fast as Christa, then Christa lost the greatest percentage of her planned laps since she was completing laps more slowly than the other two.
The exact numbers in that case are the following:
Christa: 18 x .60 = 10.8 laps, 40% lost
Jada: 2 x 10.8 = 21.6 laps, (25 - 21.6)/25 = 3.4/25 = 13.6% lost
Yvette: 2 x 10.8 = 21.6 laps, could have completed over 20 laps, 0% lost
Insufficient.
2) Cm = 75, Jm = 60, Ym = 50This choice gives us a way to determine the relative percentages of their swimming they would have completed in the same amount of time.
If Christa lost 40% of her planned time, then she must have swum for 60% of her planned time.
So, Christa swam for .60 x 75 = 45 minutes.
Also, since Christa lost 40% of her planned time, she lost 40% of her laps.
Since they all swam for the same amount of time, we know that Jada swam for 45 minutes as well. 45 minutes is 75% of the 60 minutes she planned to swim at a constant rate. Swimming at a constant rate for 75% of the time she planned to swim, she completed 75% of her laps.
So, Jada lost 25% her laps.
We also know that Yvette swam for 45 minutes, which is 90% of the 50 minutes she planned to swim.
So, Yvette lost 10% of her laps.
Thus, we can determine that Christa lost the greatest percentage of her planned laps.
In fact, we didn't even need to do these calculations. As soon as we saw that we had the amounts of time for which they planned to swim, we could tell that we could determine the relative percentages of their laps they completed since they all swam for the same amount of time. After, the one who planned to swim for the longest would have completed the smallest percentage of her laps.
Sufficient.
Correct Answer