Question

jamal works as an electricians apprentice. he rewired 4 electrical outlets in ( 1\frac{1}{2} ) hours. if he works at the same pace for 7.5 hours, how many outlets will he rewire?
( circ ) 5 outlets
( circ ) 13 outlets
( circ ) 20 outlets
( circ ) 30 outlets

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{1}{2}\) hours to an improper fraction. \(1\frac{1}{2}=\frac{3}{2}\) hours.

Step2: Find the rate of outlets per hour

The rate \(r\) is the number of outlets divided by the time taken. So, \(r = \frac{4}{\frac{3}{2}}\). Using the rule of dividing by a fraction (\(\frac{a}{\frac{b}{c}}=a\times\frac{c}{b}\)), we get \(r = 4\times\frac{2}{3}=\frac{8}{3}\) outlets per hour.

Step3: Calculate outlets in 7.5 hours

Now, we need to find the number of outlets \(n\) in 7.5 hours. First, convert 7.5 to a fraction: \(7.5=\frac{15}{2}\) hours. Then, use the formula \(n = r\times t\), where \(t=\frac{15}{2}\) hours. So, \(n=\frac{8}{3}\times\frac{15}{2}\). Simplify the fractions: \(\frac{8\times15}{3\times2}=\frac{120}{6} = 20\).

Answer:

20 outlets