SOLUTION: 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 Madel

Algebra.Com
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.

RELATED QUESTIONS

Madeline made a certain trip by moped in 2 hours. It took her 2.5 hours to make the... (answered by josgarithmetic)
One morning Madeline drove 5 hours before stopping to eat. After lunch, she increased her (answered by stanbon,josmiceli)
Isabella rode her bike at a constant speed. It took her 2 hours to travel 216km with the... (answered by richwmiller)
It took Cindy 2 hours to bike from Abbott to Benson at a constant speed. The return trip (answered by richwmiller)
It took Gina 1.8 hours to drive to her​ mother's house on Saturday morning. On her... (answered by josgarithmetic)
It took Cathy 1.8 hours to drive to her​ mother's house on Monday morning. On her... (answered by josgarithmetic)
mary drove 138 miles one way to visit her mother which took 2 1/2 hours. The return trip... (answered by ankor@dixie-net.com)
karuin motorcycle traveled 30 miles at a certain speed. had gone 10mph faster, she could... (answered by josmiceli)
An aircraft carrier made a trip to Guam and back. The trip there took three hours and the (answered by ankor@dixie-net.com)