Anne & Tom competed in the 200m long distance swimming race. After the first 50 meters, Anne had gained 2 seconds against Tom's time. Over the next three laps, Tom gained 1.5 seconds, then lost 2.1 seconds and then gained 1.7 seconds. Who is the winner and by how much?
To determine the winner and the difference in their times, let's calculate the net time difference between Anne and Tom at the end of the race.
We know that after the first 50 meters, Anne had gained 2 seconds against Tom's time. Let's represent Anne's time after the first 50 meters as A1 and Tom's time as T1.
So, A1 = T1 + 2 seconds.
Now, we need to calculate the total time for each competitor over the remaining three laps. Let's assume the duration in seconds for each lap as follows:
Anne's 2nd lap time: A2
Tom's 2nd lap time: T2
Anne's 3rd lap time: A3
Tom's 3rd lap time: T3
Anne's 4th lap time: A4
Tom's 4th lap time: T4
According to the information given, we can express A2 as T2 + 1.5 seconds, A3 as T3 - 2.1 seconds, and A4 as T4 + 1.7 seconds.
Now, let's calculate the total time for each competitor:
Anne's total time = A1 + A2 + A3 + A4
Tom's total time = T1 + T2 + T3 + T4
Substituting the values we have:
Anne's total time = T1 + 2 + (T2 + 1.5) + (T3 - 2.1) + (T4 + 1.7)
Tom's total time = T1 + T2 + T3 + T4
Simplifying the equations:
Anne's total time = T1 + T2 + T3 + T4 + 3.1 seconds
Tom's total time = T1 + T2 + T3 + T4
Since the total time of Tom is less than Anne's total time by 3.1 seconds, Tom is the winner. To find out the exact difference, we can subtract the total time of Anne from Tom:
Difference = Tom's total time - Anne's total time
Difference = (T1 + T2 + T3 + T4) - (T1 + T2 + T3 + T4 + 3.1)
Difference = -3.1 seconds
Therefore, Tom is the winner by a time difference of 3.1 seconds.