Answer:
His original speed was 60 mph.
Explanation:
The average speed formula is shown below:
speed = distance / time
For the first leg of the trip Mr. Blue drove at a speed of "x" mph, for a distance of 105 miles, therefore the time that took to complete the trip is:
time 1 = distance / speed
time 1 = 105 / x h
On the second leg of the trip Mr. Blue drove faster at a speed of "x + 10" mph, so the time it took him to complete the trip was 15 minutes less, therfore:
time 2 = time1 - (15/60) = (105/x) - 0.25 = (105 - 0.25*x)/x h
Applyint the time and speed from the second leg to the average speed formula we have:
x + 10 = {105/[(105 - 0.25*x)/x]}
x + 10 = 105*x/(105 - 0.25*x)
(x + 10)*(105 - 0.25*x) = 105*x
105*x + 1050 -0.25*x² - 2.5*x = 105*x
-0.25*x² -2.5*x + 1050 = 0 /(-0.25)
x² + 10*x - 4200 = 0
x1 = [-(10) + sqrt((10)² - 4*(1)*(-4200))]/2 = 60
x2 = [-(10) - sqrt((10)² - 4*(1)*(-4200))]/2 = -70
Since his speed couldn't be negative the only possible value was 60 mph.