Question 1151330: Madeline made a certain trip by moped in 2 hours. It took her 2.5 hours to make the return trip, since her average speed returning was 12 km/h less than her speed going. Find Madeline's average speed in each direction.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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
-----------------------------------------------------
Answers:
The speed for the 2 hour trip was 60 km/hr
The speed for the 2.5 hour trip was 48 km/hr
--------------
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.
|
|
|
