on a 75 mile trip, Mr.Jones average rate for the first 15 miles was 10 miles per hour less than his average rate for the remainder of the trip. His time for the entire trip was two hours. Find his average rate for the first 15 miles.
+128475 Distance / rate = total time
So
time for first 15 miles + time for last 60 miles = 2 hrs ....so.....
15 / r + (75 - 15) / ( r + 10) = 2 simplify
15 / r + 60 / (r + 10) = 2
15 ( r + 10) + 60r
_______________ = 2
r ( r + 10)
15r + 150 + 60r = 2 r ( r + 10)
75r + 150 = 2 ( r^2 + 10r)
75r + 150 = 2r^2 + 20r rearrange as
2r^2 - 55r - 150 = 0 factor as
(2r + 5) ( r - 30) = 0
The second factor set to 0 gives us what we need
r - 30 = 0
r = 30 (mph) = the rate during the first 15 miles
