1. ## Speed problem

Alex the geologist is in the desert, 10 km from a long, straight road and 45 km from base camp. The base camp is also 10 km from the road, on the same side of the road as Alex is. On the road, the jeep can do 50 km/h, but in the desert sands, it can only manage 30 km/h. Alex wants to return to base camp as quickly as possible. How long will the trip take?

2. Originally Posted by chil2e

Alex the geologist is in the desert, 10 km from a long, straight road and 45 km from base camp. The base camp is also 10 km from the road, on the same side of the road as Alex is. On the road, the jeep can do 50 km/h, but in the desert sands, it can only manage 30 km/h. Alex wants to return to base camp as quickly as possible. How long will the trip take?
Suppose Alex moves a distance x km on sand from starting point to the road and from road to base camp.
The distance traveled on the road will be 45 - 2*sqrt[(x^2) - (10)^2]
Time taken by him on the sand = 2x/30 h.
Time taken by him on the on the road = { 45 - 2*sqrt[(x^2) - (10)^2]}/50
Find the total time T.
To find the minimum distance traveled on sand, find dT/dx and equate it to zero. Once you find x, you can find the minimum time taken by Alex to reach the base camp.