SOLUTION: It takes a passanger train 5 hr less time than it takes a freight train to make the trip from Picture Rock to Shelbyville. The passanger train averages 90mph while the freight trai

Algebra ->  Linear-equations -> SOLUTION: It takes a passanger train 5 hr less time than it takes a freight train to make the trip from Picture Rock to Shelbyville. The passanger train averages 90mph while the freight trai      Log On


   

Question 146139: It takes a passanger train 5 hr less time than it takes a freight train to make the trip from Picture Rock to Shelbyville. The passanger train averages 90mph while the freight train averages 60 mph. Find the distance from Picture Rock to Shelbyville.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since "takes a passanger train 5 hr less time than it takes a freight train" this means that we have the equation: t%5Bp%5D=t%5Bf%5D-5

d=rt Start with the distance-rate-time formula



Let's set up the equation for the passenger train
d=90t%5Bp%5D Plug in r=90 and t=t%5Bp%5D.


d=90%28t%5Bf%5D-5%29 Plug in t%5Bp%5D=t%5Bf%5D-5


d=90t%5Bf%5D-450 Distribute



Now let's set up the equation for the freight train

d=60t%5Bf%5D Plug in r=60 and t=t%5Bf%5D.


90t%5Bf%5D-450=60t%5Bf%5D Now replace "d" with 90t%5Bf%5D-450



90t%5Bf%5D=60t%5Bf%5D%2B450 Add 450 to both sides.


90t%5Bf%5D-60t%5Bf%5D=450 Subtract 60t%5Bf%5D from both sides.


30t%5Bf%5D=450 Combine like terms on the left side.


t%5Bf%5D=%28450%29%2F%2830%29 Divide both sides by 30 to isolate t%5Bf%5D.


t%5Bf%5D=15 Reduce.


So it takes 15 hours for the freight train to arrive



d=60t%5Bf%5D Go back to the freight train speed equation


d=60%2815%29 Plug in t%5Bf%5D=15


d=900 Multiply

So the distance is 900 miles