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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
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.
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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