You traveled three hours at a certain speed. If you had taken 1 minute less to do each mile you would have gone 30 miles farther than you actually did.

How far did you go?

Answer: I went 60 miles in three hours.

Let t be the actual minutes it took me to go a mile.  

Then my mph speed was actually 60/t mph. In 3 hours I actually travelled x miles.

3*(60/t) = x 

If I had been 1 minute faster per mile, then my hypothetical speed would have been 60/(t-1) mph.

At 60/(t-1) mph, in 3 hours I would have covered 3*(60/(t-1)) miles

3*(60/t) = x  

3*(60/(t-l)) = x + 30

180/t = x

180/(t-1) = x + 30

180/(t-1) = 180/t + 30

t(t-1)[180/(t-1)] = t(t-1)[180/t] + 30t(t-1)

180t = 180(t-1) + 30t(t-1)

180t = 180t - 180 + 30t^2 - 30t

30t^2 - 30t - 180 = 0

t^2 - t - 6 = 0

(t+2)(t-3)=0

t=3

I was travelling at 60/3 = 20 mph. In 3 hours I went 60 miles. 

[I covered each mile in 3 minutes. If it had only taken me 2 minutes to cover a mile, I'd have been travelling at 30 mph, and would have gone 90 miles (90 = 60 + 30) in 3 hours.]    

 

 

 

 

 

Edited on November 29, 2004, 2:53 pm

Posted by Penny on 2004-11-29 14:09:30