imogene's car traveled 336 mi averaging a certain speed if the car had gone 6 mph faster the trip would have taken 1 hour less find the average speed

Question

imogene's car traveled 336 mi averaging a certain speed if the car had gone 6 mph faster the trip would have taken 1 hour less find the average speed

Answer 1

The key to solving word (story) problems is to correctly translate the phrases into concise, precise math expressions (variables and operations).

Now, PLZ pay attention to the units:   mile-per-hour* hours = miles
                So,      hours = miles / miles-per-hour    

                     (note: in this problem the miles are the same)

Assign variables:
        S = average speed we need to find

Translating:
       “imogene's car traveled 336 mi averaging a certain speed”    means
                                                                                       336 mi / S mph = hours
       “if the car had gone 6 mph faster”      means             (336 mi) / (S+6 mph)
“the trip would have taken 1 hour less”     means       336 / ( S + 6)  =  (336/S) -1
                                                The hours for hypothetical trip = hours for actual trip - 1
“find the average speed”     means     report S

O.K., now the math:
     336 / (S + 6)   = (336/S) – 1
     336*S = -S^2 + 330 S + 2016                       cross multiplying
      S^2 +6*S – 2016  = 0
      (S+48)(S-42) = 0                           factor or use quadratic equation
       S = -48 or 42       but S must be positive,  so S = 42 mph

Checking:
     Is 336/48 = 336/42 – 1    ?
         7  =  7      Yes.