A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8 hours in the afternoon, how many hours does she work in the evening?
or ..
she works 1.75 hours longer in the evenings
so time worked in evening = 5 1/8 + 1.75 hours
= 5.125 + 1.75 hours
= 6.875 hours or 55/8 or 6 7/8 hours if you want it in fractions
To find out how many hours the waitress works in the evening, we need to calculate the total hours she works in the afternoon.
Given that she works 1.75 hours less in the afternoon than in the evening, we can express the evening hours as x hours. Therefore, the afternoon hours would be x - 1.75 hours.
It is provided in the question that she works 5 1/8 hours in the afternoon, which is equivalent to 5 + 1/8 = 41/8 hours.
Setting up an equation, we can write:
x - 1.75 = 41/8
To solve for x, we can simplify and solve this equation.
First, let's add 1.75 to both sides of the equation:
x - 1.75 + 1.75 = 41/8 + 1.75
This simplifies to:
x = 41/8 + 14/8
Adding the fractions:
x = 55/8
Therefore, the waitress works 55/8 hours in the evening.
To convert this improper fraction to a mixed number, we perform division:
55 รท 8 = 6 with a remainder of 7
Hence, the waitress works 6 7/8 hours in the evening.
Let's denote the number of hours the waitress works in the evening as E.
Given that she works 1.75 hours less in the afternoon than in the evening, we can express this as:
Afternoon time = Evening time - 1.75 hours
We also know that she works 5 1/8 hours in the afternoon, which can be written as:
Afternoon time = 5 + 1/8 hours
Equating the two expressions for afternoon time, we have:
5 + 1/8 = E - 1.75
To solve for E, we can start by adding 1.75 to both sides of the equation:
5 + 1/8 + 1.75 = E
Converting the mixed number 5 1/8 to an improper fraction:
5 + 1/8 = 40/8 + 1/8 = 41/8
Substituting this value into the equation, we have:
41/8 + 1.75 = E
To simplify the expression, let's convert 1.75 to an improper fraction:
1.75 = 1 + 3/4 = 4/4 + 3/4 = 7/4
Adding the fractions:
41/8 + 7/4 = 41/8 + (7/4) * (2/2) = 41/8 + 14/8 = 55/8
Therefore, the waitress works 55/8 hours in the evening.