Problema Solution
Jon recently drove to visit his parents who live 270 miles away. On his way there his average speed was 24 miles per hour faster than on his way home. If jon spent a total of 12 hours driving, find the two rates.
Answer provided by our tutors
Jon drove to visit his parents who live = 270 miles away
On his way the speed was = say x miles/hour
On his way to hom the speed was =y = x+24 miles/hour
Totally he drove for 12 hour (both to and fro).
270 = xt1
270= (x+24)*t2
t1+t2=12
270/x +270/(x+24) = 12
135 (1/x + 1/(x+24)) = 6
135 (x+12)/x(x+24) = 3
135x+135*12 = 3x^2+24*3x
3x^2-63x-1620=0
x= 63+/- sqrt(3969+19440) /6 = 36 miles/hour
y = 36+24 = 60 miles/hour