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6. Solution

time taken = distance traveled / speed

let the distance to Phoenix = d

time to Phoenix = t = d / 80

d = 80t... [eqn 1]

Time to return = t + 1 = d / 70 ... [eqn 2]

(a) subs [eqn 1] into [eqn 2] → t + 1 = (80t) / 70

70t + 70 = 80t

10t = 70

t = 7

so the total traveling time (for return trip) = 7 + 7 + 1 = 15 h

b) subs t = 7 into [eqn 1] → d = 80 * 7 = 560

so she lives 560 miles from Phoenix

______________speed____________time______________distance

going_________g________________t_________________d

returning_____r________________t-k_______________d

Known variables: g, r, k

Unknown variables: t, d

Variables Assigned as g=60, r=75, k=1

Equations possible from data:

, and ;

The system is linear for t and for d. The simplest thing to do is equate the two expressions for d, and first solve for t.

7. Solution

Let geoffrey drove g mph on the way to visit his parents. on the way back to school he drove r mph and it took him k hour less time then it did to drive to his parents house.

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