Alex in the Desert

Alex the geologist is in the desert, 10 miles from a long, straight road. On the road, Alex's jeep can go 50 miles per hour, but in the desert sands, it can only go 30 miles per hour. Alex is very thirsty and wants to buy some lemonade at a gas station which is 20 miles down the road from the point on the road, N, nearest to Alex. If Alex takes the fastest route possible, it will take only 40 minutes to get to the gas station and sip some cool lemonade. What route should Alex take?

Alex in the Desert 1

The next day, Alex the geologist is back in the desert, investigating a new location which is also 10 miles away from the same road. But this time, the point on the road nearest to Alex, M, is 30 miles away from the Gas Station. If Alex gets a hankering for a lemonade again, the fastest route to the gas station will take 52 minutes. What route should Alex take?

Alex in the Desert 2