Question

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.

Answer 1

Ruby worked 18 hours, Isaac worked 12, and Svetlana worked 72

Explanation:

let:

- r : the amount of hours ruby worked

- i : the amount of hours isaac wcorked

- s : the amount of hours svetlana worked

given:

1) ruby worked 6 hours more than isaac

this translates to equation (1) r = i + 6

2) svetlana worked 4 times as many hours as ruby

this translates to equation (2) s = 4 * r

3) Together they worked 102 hours

this translates to r + i + s = 102 for equation (3)

Now, isolate i from (1) to get i = r - 6, and replace i in (3) using this:

r + (r - 6) + s = 102.

This equals -> 2r + s = 102 + 6 -> 2r + s = 108

replace s here with s from (2): 2r + (4*r) = 108

this equals 6*r = 108, from here, isolate r: r = 108/6 = 18

we know that i = r - 6. So i = 18 - 6 = 12

And s = 4*r = 4*18 = 72

verify that this works -> 72 + 18 + 12 = 102.