Word problem help

Question

it took Roman 10 hours to drive to a family reunion on the way home he was able to increase his average speed but 18 mph and make the return drive in only 7 hours. find his average speed on the return drive

Answer 1

d = r · t

 

On the way there

d = r · 10

 

On the way back

d = (r + 18)7

 

The distance there and back is the same

10r = 7(r + 18)

10r = 7r + 126

3r = 126

r = 42

r + 18 = 60

Answer 2

Well, first remember "Distance Is Rate times Time"    (a.k.a., D-I-R-T, you know, dirt)
 
In this problem, we don't need to find the distance, but we know that going "to" is the same distance as coming "from".
 
   Let X = speed of return trip  (the value we want to find)
 
Coming from:     D = X mi/hr * 7 hrs
Going to:      D = (X -18) mi/hr * 10 hr       (18 mph slower)

                    D = X*7 = (X-18)*10        (first D = second D)
                             7X = 10X - 180
                               -3X = -180
                                X = 60 mph 
Checking:
         Is  60*7 = (42)*10    ?     Yes.