Question 1151330
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Let's say Madeline goes from point A to B and it takes her 2 hours. Her speed is some unknown, which we'll call x km/hr. 


When she goes from B to A, it takes her 2.5 hours and her speed is (x-12) km/hr. 
Both trips travel the same distance (assume she takes the same roads for both trips), which we'll call d.


Going from A to B
distance = rate*time
d = x*2
d = 2x


Going from B to A
distance = rate*time
d = (x-12)*2.5
d = 2.5x - 30


Because 'd' is the same for both equations, we can use substitution and solve for x.
d = 2.5x - 30
2x = 2.5x - 30 .... replace d with 2x
2x-2.5x = -30
-0.5x = -30
x = -30/(-0.5)
x = 60


Now we know that x = 60, we can say,
x-12 = 60-12 = 48


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Answers:
The speed for the 2 hour trip was <font color=red size=4>60 km/hr</font>
The speed for the 2.5 hour trip was <font color=red size=4>48 km/hr</font>


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Check:
If Madeline travels for 2 hours at 60 km/hr, then she covers a distance of
d = r*t = 60*2 = 120 km
If Madeline travels for 2.5 hours at 48 km/hr, then she covers a distance of
d = r*t = 48*2.5 = 120 km
She covers the same distance both ways, which helps us confirm we have the right answers.
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