One month, ruby worked for 6 hours more than isaac, and svetlana worked 4 times as many hours as ruby. together they worked 126 hours. find the number of hours each person worked

Ruby worked 22 hours

Isaac worked 16 hours

Svetlana worked 88 hours

Call the number of hours that Isaac worked x.

Ruby worked x+6, because she worked 6 hours more than Isaac.

Svetlana worked 4(x+6), because she worked 4 times as many hours as Ruby.

All together, Isaac, Ruby, and Svetlana worked 126 hours.

You can add all of the amounts that they worked together in an equation to find how much is x:

x+x+6+4(x+6)=126

Distribute.

x+x+6+4x+24=126

Combine like terms.

6x+30=126

Subtract 30 from both sides.

6x=96

Divide both sides by 6.

x=16

Isaac worked 16 hours. Now, you can plug 16 in for x to find how much Ruby and Svetlana worked.

Ruby worked x+6 hours=16+6 hours=22 hours.

Svetlana worked 4(x+6) hours=4(16+6)=64+24 hours=88 hours

You can add all of their times together to make sure it equals 126 hours:

16+22+88=126

Isaac worked 16 hours; Ruby worked 22 hours; Svetlana worked 88 hours.

I hope this helps :)

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.