optimal values for composite function models!!! :S?

Question

A dune buggy is on a straight desert road, 40 km north of Dustin city. The vehicle can travel at 45 km/h off the road and 75 km/h on the road. The driver watns to get to Gulch City, 50 km east of Dustin by another straight road, in the shortest possible time. Determine the route he should take.

ur supposed to find the optimal value by using a composite function. Thanks :)

Answer 1

t = (1/45)(40^2 + x^2)^(1/2) + 50/75 - x/75
t' = x(1/45)(40^2 + x^2)^(-1/2) - 1/75 = 0 for min
(40^2 + x^2)^(-1/2) = 45/75x
(40^2 + x^2)^(1/2) = 5x/3
40^2 + x^2 = 25x^2/9
9*40^2 + 9x^2 = 25x^2
16x^2 = 9*40^2
4x = 3*40
x = 30 km E. of Dustin
Drive in a straight line at 45 kph to a point 30 km E. of Dustin. Then proceed at 75 kph on the last 20 km of the Dustin-Gulch City road.
The distance at 45 kph is 50 km
The time is 50/45 + 20/75 = 1 hr 22 min 40 sec

Unfortunately, the time by road is (40 + 50)/75 = 90/75 = 1.2hr = 1 hr 12 min, so the route for minimum time is on the roads all the way.

Answer 2

the question may be wrong!