SOLUTION: jon recently drove to visit his parents who live 456 miles away on his way there his average speed was 14 mph faster than his drive there. jon spent a total of 19 hours driving

Question 931844: jon recently drove to visit his parents who live 456 miles away on his way there his average speed was 14 mph faster than his drive there. jon spent a total of 19 hours driving
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
jon recently drove to visit his parents who live 456 miles away
on his way there his average speed was 14 mph faster than his drive back.
jon spent a total of 19 hours driving
:
Assume you are looking for his average speed
:
let s = his speed to his parents
then
(s-14) = his return speed
;
write a time equation; time = dist/speed
+ = 19
multiply eq by s(s-14), cancel the denominators and you have
456(s-14) + 456s = 19s(s-14)
456s - 6384 + 456s = 19s^2 - 266s
912s - 6384 = 19s^2 - 266x
a quadratic equation
19s^2 - 266s - 912s + 6384 = 0
19s^2 - 1178s + 6384 = 0
using the quadratic formula I got
s = 6
s = 56, obviously the only reasonable answer
:
He went 56 mph there and returned at 42 mph (14 mph less)
:
:
See if that checks out; find the actual time each way
456/56 = 8.143 hrs
456/42 = 10.857 hrs
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total time 19.00 hrs?
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