SOLUTION: Thaddeus and Ian start at the same location and drive in opposite directions, but leave at different times. When they are 270 miles apart, their combined travel time is 8 hours.

Question 1036035: Thaddeus and Ian start at the same location and drive in opposite directions, but leave at different times. When they are 270 miles apart, their combined travel time is 8 hours.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.

let a be the time it takes thaddeus.
let 8 - a be the time it takes ian.
let c be the distance that thaddeus travels.
let 270 - c be the distance that ian travels.

the rate * time formula for thaddeus becomes 30 * a = c
the rate * time formula for ian becomes 35 * (8 - a) = (270 - c)

their combined formula becomes:

30 * a + 35 * (8 - a) = c + (270 - c)

simplify this formula to get:

30 * a + 35 * 8 - 35 * a = c + 270 - c

simplify further and combine like terms to get:

-5 * a + 280 = 270

subtract 280 from both sides of this formula to get:

-5 * a = -10

divide both sides of this formula to get:

a = 2

since a = 2, then 8 - a must be equal to 6.

the formula for thaddeus becomes 30 * 2 = c
the formula for ian becomes 35 * 6 = 270 - c

in the first formula, solve for c to get c = 60.
in the second formula, solve for 270 - c to get 270 - c = 210.

the formulas become:

30 * 2 = 60
35 * 6 = 210

thaddeus traveled 60 miles in 2 hours.
ian traveled 210 miles in 6 hours.

you were asked how long each was driving.

thaddeus was driving for 2 hours and ian was driving for 6 hours.

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