how far away live from the mountains?

Question

trip took 6 hours. there was no traffic and the trip only took 4 hours. average rate was 22 miles per hour faster on the trip home, how far away live from the mountains?

 

Do not do any rounding.

Answer 1

Matt,

 

Let          s = average speed (mph) traveling toward the mountains.

    (s + 22) = average speed coming home (mph)

               t = travel time (in hours) ; 6 hours to mountains and 4 hours home.

          d(t)  = distance traveled after t hours.  = average speed x time

 

To the mountains, d(6) = s(6) = 6s.

Toward home,  d(4) = (s + 22)(4) = 88 + 4s  , but the distance is identical going there and coming back

 

So      6s = 88 + 4s      and  2s = 88.     Thus,  s = 44 mph going there and 66 mph coming back

And  d(6) = 6 (44) = 264 miles.