SOLUTION: 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?

Question 65597This question is from textbook An Incremental Development
: 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? This question is from textbook An Incremental Development

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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
Ck
By inspection we see that Ortiz travelled twice as fast and made the trip in five hours less time than his brother
Hope this helps -----ptaylor

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