SOLUTION: Please help with this. Judy averaged 42 miles per hour(mph) driving from Allentown to Harrisburg and 51 mph driving from Harrisburg to Pittsburg. If she drove a total of 288 mile

Question 165221: Please help with this.
Judy averaged 42 miles per hour(mph) driving from Allentown to Harrisburg and 51 mph driving from Harrisburg to Pittsburg. If she drove a total of 288 miles in 6 hours, then how long did it take her to drive from Harrisburg to Pittsburg?
I set this up a 2 equations using a chart as: Distance Speed Time
Allentown to Harrisburg x 42 42x
Harrisburg to Pittsburg y 51 51y
Allentown to Pittsburg 288 288/6=48 6

Now x + y = 288
42x + 51y = 6 by substitition using y = 288 - x

42x + 51(288-x) = 6
42x + 14,688 -51x = 6
-9x = -14,682 and x = 1631.33
It works out when you plug back in, but can't be true since there is a total of only 288 miles. The y then is a negative number which satisfies the equation. Pleas help. Thanks Claudia
TheISBN shows: ISBN-13: 978-0-07-326862-0
ISBN-10: 0-07-326862-3
Part of
ISBN-13: 978-0-07-326938-2
ISBN-10: 0-07-326938-7
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
rt=d __ you have the rates, the total time and the total distance

let x="time from Harrisburg to Pittsburg", so 6-x="time from Allentown to Harrisburg"

51(x)+42(6-x)=288 __ 51x+252-42x=288 __ 9x=36 __ x=4
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