The time required to complete a job varies inversely as the number of people working. it took 4 hours for 7 electricians to wire a building. how long would it have taken 3 electricians to have done the job?

Let's assign variables

The time required to wire a building: y

The number of electricians to have done this job: x


y varies inversely as x

so that:

where  k is the proportional constant

To calculate the value of k, plug in the values of x and y:
x=7
y=4



Now, write down the relation between x and y:


"how long would it have taken 3 electricians to have done the job?"
x=3
Let's find out y:


So it would take 9 hours and 20 minutes to have this job done.

Given: m∠ABC=(6x+8)° and m∠DEF=(12x−8)°.

To find: measure of angles m∠ABC and m∠DEF.

Soltution: It is said ∠ABC and ∠DEF are supplementary.

Sum of supplementary angles is 180°.

So, we can add the given values of angles ∠ABC and ∠DEF and set it equal to 180°.

m∠ABC +  m∠DEF= 180°

Plugging values of ∠ABC and ∠DEF in above equation.

(6x+8)  + (12x−8) = 180.

Removing parenthese,

6x+8 +12x - 8 = 180.

Combining like terms

6x+12x = 18x and 8-8 = 0.

Therefore, 6x+8 +12x - 8 = 180 would become 18x  = 180.

Dividing both sides by 18, we get

18x/18 = 180/18

x=10.

Plugging value of x in given expessions for m∠ABC and m∠DEF.

m∠ABC=6x+8 = 6* 10 +8 = 60 +8 = 68.

m∠DEF=12x−8 = 12*10 -8 = 120 - 8 = 112.

Therefore, m∠ABC= 68° and m∠DEF =112° .