Ortiz drives twice as fast as his brother and therefore make

Ortiz drives twice as fast as his brother and therefore makes the 350-mile trip home in 5 hours less time. How fast does each drive, and for how long does each travel?

Solution

Let r= Oritz brothers rate of speed
Then 2r=Ortiz rate of speed
We\'ll let t=Oritz brothers time for the trip
Then t-5=Ortiz time for the trip
Now we know that distance (d)=rate(r) times time (t)
We also know that d=350 mi
(r)(t) =distance Ortiz brother travels =350 mi
2r(t-5)=distance Ortiz travels =350 mi
So our equations to solve are:
rt=350
2r(t-5)=350
Since both equations equal 350 mi we have:
rt=2r(t-5)
rt=2rt-10r simplifying we have:
2rt-rt=10r
rt=10r
t=10 hours Ortiz brothers travel time
t-5=10-5=5 hours Ortiz travel time
Now rt=350
r(10)=350
r=35 MPH Oritz brothers rate of speed
2r=2(35)=70 MPH Ortiz rate of speed