the school's track team ran the 220 relay in 7 minutes 46 seconds at their first track meet. The next meet, their time was 42 seconds shorter. At the next, their improvement was twice as great. What was their total running time at the last met?
meet 1: 7'46"
meet 2: 7'46" - 42" = 7'04"
next meet the reduction was 2*42 = 84 seconds
meet 3: 7'04" - 84" = 5'40"
Well, it seems like the school's track team is on a roll! If their first time was 7 minutes and 46 seconds, and the next meet was 42 seconds shorter, that means their second time was 7 minutes and 4 seconds. Now, if their improvement at the third meet was twice as great, we'll double the 42-second improvement to get 84 seconds.
So, the third time will be 7 minutes (since there are 60 seconds in a minute) and 4 seconds (from the previous meet), minus 84 seconds.
Now, let me do some quick calculations on my imaginary abacus... Ta-da! The total running time at the last meet is 6 minutes and 20 seconds. The team is really speeding up!
To find the total running time at the last meet, we can follow these steps:
Step 1: Calculate the time difference at the second meet.
The time at the second meet is 42 seconds shorter than the time at the first meet.
So, the time difference at the second meet is 7 minutes 46 seconds - 42 seconds.
Step 2: Calculate the time at the second meet.
To calculate the time at the second meet, we subtract the time difference from the time at the first meet.
Time at the second meet = (7 minutes 46 seconds) - (42 seconds).
Step 3: Calculate the time difference at the third meet.
The improvement at the third meet is twice as great as the improvement at the second meet.
So, the time difference at the third meet is 2 * (time difference at the second meet).
Step 4: Calculate the time at the third meet.
To calculate the time at the third meet, we subtract the time difference at the third meet from the time at the second meet.
Time at the third meet = (time at the second meet) - (time difference at the third meet).
Step 5: Add up the times at all the meets.
Total running time at the last meet = (time at the first meet) + (time at the second meet) + (time at the third meet).
Now, let's calculate the values step by step.
Step 1:
Time difference at the second meet = 7 minutes 46 seconds - 42 seconds.
Time difference at the second meet = 7 minutes 4 seconds.
Step 2:
Time at the second meet = (7 minutes 46 seconds) - (42 seconds).
Time at the second meet = 7 minutes 4 seconds.
Step 3:
Time difference at the third meet = 2 * (time difference at the second meet).
Time difference at the third meet = 2 * (7 minutes 4 seconds).
Step 4:
Time at the third meet = (time at the second meet) - (time difference at the third meet).
Time at the third meet = (7 minutes 4 seconds) - (14 minutes 8 seconds).
Note that it is important to convert minutes and seconds to the same units before subtracting.
Step 5:
Total running time at the last meet = (time at the first meet) + (time at the second meet) + (time at the third meet).
Now, perform the calculations to get the final answer.
To get the total running time at the last meet, we first need to find the time it took at the second meet and then at the third meet.
Let's start by calculating the time it took at the second meet:
The team ran the 220 relay in 7 minutes 46 seconds at the first meet.
Their time at the next meet was 42 seconds shorter.
To find the time at the second meet, we can subtract 42 seconds from the time at the first meet.
7 minutes 46 seconds - 42 seconds = 7 minutes 4 seconds
Therefore, at the second meet, the team ran the 220 relay in 7 minutes 4 seconds.
Now, let's calculate the time at the third meet:
The improvement at the third meet was twice as great as the improvement at the second meet.
To find the time at the third meet, we need to double the improvement from the second meet and subtract it from the time at the second meet.
Improvement at the second meet: 42 seconds
Double the improvement: 2 * 42 seconds = 84 seconds
7 minutes 4 seconds - 84 seconds = 6 minutes 20 seconds
Therefore, at the third meet, the team ran the 220 relay in 6 minutes 20 seconds.
To find the total running time at the last meet, we need to sum the times from all three meets:
7 minutes 46 seconds (first meet) + 7 minutes 4 seconds (second meet) + 6 minutes 20 seconds (third meet)
Coming up with a total of:
21 minutes 10 seconds
Therefore, the team's total running time at the last meet was 21 minutes 10 seconds.