SOLUTION: Serge usually drives from his home to MSU-IIT in 12 minutes. When in a hurry, he increases his average speed by 5km. per hour and makes the trip in 10 minutes. How far does Serge l

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Serge usually drives from his home to MSU-IIT in 12 minutes. When in a hurry, he increases his average speed by 5km. per hour and makes the trip in 10 minutes. How far does Serge l      Log On

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Question 1007453: Serge usually drives from his home to MSU-IIT in 12 minutes. When in a hurry, he increases his average speed by 5km. per hour and makes the trip in 10 minutes. How far does Serge live from MSU-IIT?
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
In general, distance = rate * time, or d=rt.
Here, t = d/r = 12 minutes = 1/5 hour.
This means d = 1/5r.
In a hurry, we have (10 minutes is 1/6 hour)
d/(r+5) = 1/6 or
d = (1/6)(r+5)
Since the distance is the same we can set them equal and get
(1/5)r = (1/6)(r+5)
(1/5)r = (1/6)r + 5/6
(6/30)r = (5/30)r + 5/6
(1/30)r = 5/6
r = 25 km/hr
and since d = rt we have
d = (25)(1/5) = 5 km