Gretchen, Miranda and Ariel worked a total of 105 hours this week. If the ratio of Gretchen's hours to Miranda's to Ariels is 1:4:2, what is the difference between the number of hours Miranda worked and the number of hours Ariel worked?
How many hours did each work?
Total of 1:4:2 = 7. then
105 x (1/7)*100 = hours G worked.
105 x (4/7)*100 = hours M worked.
105 x (2/7)*100 = hours A worked.
Then difference between hours M - hours A = ?
To find the difference between the number of hours Miranda worked and the number of hours Ariel worked, we first need to determine the number of hours each person worked.
Let's assume that Gretchen worked x hours. According to the given ratio, Miranda worked 4x hours, and Ariel worked 2x hours. Therefore, the total number of hours worked can be represented by the equation:
x + 4x + 2x = 105
Simplifying the equation:
7x = 105
Dividing both sides by 7:
x = 15
Now we know that Gretchen worked 15 hours. By substituting this value into the ratio, we can find the number of hours Miranda and Ariel worked:
Miranda worked 4x = 4 * 15 = 60 hours
Ariel worked 2x = 2 * 15 = 30 hours
To find the difference between the hours Miranda worked and the hours Ariel worked, we subtract the two values:
Difference = Miranda's hours - Ariel's hours
Difference = 60 hours - 30 hours
Difference = 30 hours
Therefore, the difference between the number of hours Miranda worked and the number of hours Ariel worked is 30 hours.