At the end of each working day, highway police must report the total amount of time spent performing certain tasks. During one 8-hour shift, an officer spent 30 minutes aiding vehicles in distress, 1 3 over 4 hours at the scene of an accident, and 2 hours and 25 minutes writing tickets. How much time did the officer spend doing these tasks?
Select the correct answer.
Question 1 options:
4 fraction numerator 2 over denominator 3 end fraction hours
4 fraction numerator 1 over denominator 3 end fraction hours
4 fraction numerator 1 over denominator 2 end fraction hours
To find the total amount of time spent on these tasks, we need to add the time spent aiding vehicles in distress, the time spent at the scene of an accident, and the time spent writing tickets.
Converting the time spent at the scene of an accident from mixed number to improper fraction:
1 3/4 = 4/4 + 3/4 = 7/4
Converting the time spent writing tickets to an improper fraction:
2 hours and 25 minutes = 2 + 25/60 = 2 + 5/12 = 24/12 + 5/12 = 29/12
Now, adding the time spent on each task:
30 minutes = 30/60 = 1/2 hour
7/4 hours + 29/12 hours + 1/2 hour = (7/4 + 29/12 + 1/2) hours
To add the fractions, we need a common denominator, which is 12:
(7/4 + 29/12 + 1/2) hours = (21/12 + 29/12 + 6/12) hours = 56/12 hours
Simplifying the fraction:
56/12 = 4 and 2/3
Therefore, the total amount of time the officer spent on these tasks is 4 2/3 hours.
The correct answer is 4 fraction numerator 2 over denominator 3 end fraction hours.
To determine the total amount of time the officer spent doing these tasks, we need to add up the individual times.
The officer spent 30 minutes aiding vehicles in distress, which is equal to 30/60 = 1/2 hours.
The officer spent 1 3/4 hours at the scene of an accident. To add the whole numbers and fractions, we first convert the whole number to a fraction. 1 = 4/4. Then we add the fractions: 4/4 + 3/4 = 7/4 hours.
The officer spent 2 hours and 25 minutes writing tickets, which is equal to 2 + 25/60 = 2 + 5/12 = 29/12 hours.
To find the total time spent on these tasks, we add the three amounts:
1/2 hours + 7/4 hours + 29/12 hours.
To simplify the fractions, we need to find a common denominator. The common denominator for 2, 4, and 12 is 12.
1/2 hours can be rewritten as 6/12 hours.
7/4 hours can be rewritten as 21/12 hours.
29/12 hours stays the same.
Now we can add the fractions:
6/12 hours + 21/12 hours + 29/12 hours = 56/12 hours.
To simplify the fraction, we divide the numerator by the denominator:
56/12 ÷ 4/12 = 56/12 × 12/4 = 14/1 = 14 hours.
Therefore, the officer spent a total of 14 hours doing these tasks.
The correct answer is: 14 hours.
To find the total amount of time the officer spent on these tasks, we add the time spent aiding vehicles in distress (30 minutes), the time spent at the scene of an accident (1 3 over 4 hours), and the time spent writing tickets (2 hours and 25 minutes).
First, let's convert the time spent at the scene of an accident to a fraction of an hour.
1 3 over 4 hours can be converted to 1.75 hours (since 3 over 4 is the same as 0.75).
Now, let's convert the time spent writing tickets to a fraction of an hour.
2 hours and 25 minutes can be converted to 2.42 hours (since 25 minutes is the same as 0.42).
Now, add the time spent aiding vehicles in distress, the time spent at the scene of an accident, and the time spent writing tickets:
30 minutes + 1.75 hours + 2.42 hours = 4.17 hours
Therefore, the officer spent 4 fraction numerator 1 over denominator 2 end fraction hours doing these tasks.