Question

julie recently drove to visit her parents who love 72 miles away. on her way there her average speed was 14 miles per hour faster than on her way home. if julie spent a total of 3 hours driving, find the two rates.

Answer 1

72 [miles]/ x[miles/h] => time she need to go home
72 [miles} / (x+14) [miles/h] => time to go to her parent's.
add then =3h
x is the variable

Answer 2

\[72/x + 72/(x+14)=3\]

Answer 3

same denominator
\[72(x+14)+72x=3*x(x+14)\]\[72*(x+14+x)=3x*(x+14)\]\[72*(2x+14)=3x²+42x\]\[144x+1008=3x²+42x\]\[3x²-102x-1008=0\]
using \[\Delta=b²-4ac\]
2 solutions
\[x=-b-\sqrt(\Delta)/2a\] or \[x=-b+\sqrt(\Delta)/2a\]
x=-8 or 42 (-8 impossible because it's a speed)
so x=42mph
and 56mph

if we check the solution
72/42 +72/56 = (72*56+72*42)/(56*42)=3
Job done