Word problems

Question

A pedestrian walked 6 miles in a certain interval of time. Had the time been 1/2 hour less, the rate would have been 2 miles per hour greater. How long did the pedestrian walk?

Answer 1

You've gotta love Rate * Time = Distance!!!!

 

Rate       Time         Distance

6/t            t                  6

6/(t-.5)     t-.5              6

 

So now, the second rate is 2 mph faster than the first rate......

 

6/(t-.5) = 6/t + 2

 

6t/t(t-.5) = 6(t-.5)/t(t-.5) + 2t(t-.5)/t(t-.5)    you can now eliminate all the common denominators to get

 

6t  =  6(t-.5) + 2t(t-.5)

6t  = 6t - 3 + 2t^2 - t

0 = 2t^2 - t - 3 

0 = (2t - 3)(t + 1)

t = 3/2 or t = -1

t = -1 will be rejected.

 

Weird answer so I'll check it

 

Times are 1.5 and  1

Rates would then be 6/1.5 and 6/1 which are 4. and 6. And look, one rate is 2 mor than the other.

 

So the pedestrian walked 4 mph.

 

Hope this helped