How do you do these?

Algebra
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Jun 2nd, 2015

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Jun 2nd, 2015

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:
gt=d, and r%28t-k%29=d;
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. 


Jun 2nd, 2015

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