Algebra 1 question

Question

I need help with this. Please show all the steps. :P

 

Hearst Castle if 180 miles from Ventura by road. Two coaches leave Ventura at the same time, both heading for Hearst Castle, but one averages 5 mph faster than the other. If the faster coach reaches Hearst Castle half an hour earlier than the slower coach, what is the average speed of the faster coach?

Answer 1

S - Speed of the fast  coach

 

d = S t 

 

 t = d 

       s

  

 180    =  180  - 1   =   360 -S   

 S +5        S      2          2S 

 

 360 S = 360 S - S² +1800 -5S

 

    S² + 5S -1800 = 0

 

    ( S + 45 ) ( S - 40 ) =0

 

       S = 40 miles /hr

 

     Test:

 

      180  = 4.5 hrs

       40 

       

       180  = 4 hrs

        45