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Question 1078779: Alex the geologist is in the desert, 10 km from the nearest point N on a long, straight
road. Alex’s jeep can do 50 kph on the road, and 30 kph in the desert. Find the shortest
time for Alex to reach an oasis that is on the road (a) 20 km from N; (b) 30 km from N
Answer by josgarithmetic(39615)   (Show Source):
You can put this solution on YOUR website! Point in the desert, point on road nearest to Alex, and line segment to where on the road he will first leave the desert form a right triangle.
If for part (a), if Alex will go to some intermediate point on the road before being able to travel on the road, his road distance is x; then the leg of the triangle , the part of the road he does NOT use, is 20-x. Alex in the desert is 10 kilometer from the road. Hypotenuse of this triangle is the length he drives in the desert to reach the road.
Total time, using the distances and jeep speeds of desert and road,
You could find  and equate to 0, and solve for x.
Once x is found, use it to evaluate T.
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note: exponent of 2 on expression inside the radical, result of using Pythagorean Theorem
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Checking with a graphing tool suggests some 12.5 kilometers for x, the length of road Alex will drive. You could use this to find total time, and also the distance Alex will travel on the desert, and the distance from point N where he leaves the desert and starts on the road.
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