How do I find the distance for this problem?

Question

Alex the geologist is in the desert, 10 km from a long, straight road. Alex’s jeep does
50 kph on the road and 30 kph in the desert. Alex must return immediately to base camp,
which is on the same side of the road, 10 km from the road, and "d" km from Alex. It so
happens that the quickest possible trip will take the same amount of time, whether Alex
uses the road or drives all the way in the desert. Find "d"

Answer 1

The key here is to sketch the question. Alex is 10 km from the road and base camp is 10 km from the road and on the same side. It is reasonable then to conclude that base camp is a straight line from where Alex is at a distance "d". The second given piece of information is that if Alex drives 10 km in the desert to the road, a distance "d" on the road and then another 10 km back in the desert to get to base camp (t1) will take THE SAME TIME as if he just drives the distance "d" in the desert (t2). Having these two pieces of information makes it simple to find the answer.

 

We know that time (t) = distance (d)/ speed (v)

and since t1 = t2 (given)

then d (km) / 30 (kph) = 10 (km) / 30 (kph) + d (km) / (50 kph) + 10 (km) / 30 (kph)

d/30 = d/50 + 2/3

5d/150 - 3d/150 = 2/3

2d/150 = 2/3

d/50 = 1

so distance "d" = 50 KM

 

check: calculate the time for both trips and you should come up with equal time that is 100 minutes or 1 hour and 40 minutes.

 

All the best