SOLUTION: Zeno, Orb, Yurko and Sam are friends who live on neighboring space stations of the planet Krayon. They commute to school every day by space shuttle. Orb's space station is one ha

Algebra ->  Expressions-with-variables -> SOLUTION: Zeno, Orb, Yurko and Sam are friends who live on neighboring space stations of the planet Krayon. They commute to school every day by space shuttle. Orb's space station is one ha      Log On


   

Question 250849: Zeno, Orb, Yurko and Sam are friends who live on neighboring space stations of the planet Krayon. They commute to school every day by space shuttle. Orb's space station is one half as far from Krayon as Zeno's space station. yurko travels as far as the total distance traveled by zeno and Orb, while sam travels three times the distance that Zeno travels. How many space miles does each friend travel to school, if the friends together travel a total of 888 space miles?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let:

z = distance zeno has to travel
o = distance that orb has to travel
y = distance that yurko has to travel
s = distance that sam has to travel.

from the problem statement:

o = z/2
y = z + o which is equivalent to z + z/2
s = 3z

total distance they trafel is 888 space miles.

this means that:

z + o + y + s = 888

substituting all values in terms of z, we get:

z + (z/2) + (z + z/2) + 3z = 888

simplifying by removing parentheses gets:

z + z/2 + z + z/2 + 3z = 888

combining like terms gets:

6z = 888

dividing both sides of the equation by 6 gets:

z = 148

o = z/2 = 148/2 = 74

y = z + o = 148 + 74 = 222

s = 3z = 444

148 + 74 + 222 + 444 = 888 confirming the answers are good.

your answer is:

zeno travels 148 space miles
orb travels 74 space miles
yurko travels 222 space miles
sam travels 444 space miles