Drag and drop numbers into the boxes to complete and solve the equation for the situation. One month, Ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby.
Together they worked 102 hours. Find the number of hours each person worked.
h
Isaac worked
hours.
Ruby worked
hours.
Svetlana worked
hours.

Isaac worked 12 hours

Ruby worked 18 hours

Svetlana worked 72 hours

Step-by-step explanation:

Here in this question, we are interested in knowing the number of hours each person worked.

We proceed as follows;

Let the number of hours Isaac worked be x hours.

From the question, we are told that Ruby worked 6 hours more than Isaac

So the number of hours Ruby worked will be;

(x + 6) hours

Also;

Svetlana worked 4 times as many as Ruby:

This means that we have to multiply the number of hours Ruby worked by 4 to get the number of hours that Svetlana worked;

So the number of hours Svetlana worked will be : 4(x + 6) hours

Since the three worked a total of 102 hours, to get the number of hours each worked, we need to add together the number of hours each individual put in to work and equate to 102;

Mathematically, that would be;

x + x + 6 + 4(x + 6) = 102

2x + 6 + 4x + 24 = 102

6x + 30 = 102

6x = 102-30

6x = 72

x = 72/6

x = 12 hours

So Isaac worked x hours = 12 hours

Ruby worked (x + 6) hours = 12 + 6 = 18 hours

Svetlana worked 4(x + 6) hours = 4(18) = 72 hours

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.