Applications of Pythagoras' Theorem in Real-World Contexts

Question

A courier travels due North at an average speed of 40 km/h for 6 minutes to collect a parcel, before travelling 10 km due East to deliver it. He then travels due South at an average speed of 30 km/h for 12 minutes to collect another parcel, Find the shortest distance between the courier and his starting point.

Answer 1

Yes, draw and label a diagram!

10 miles north

10 miles east

6 miles south

ending at 10 miles east and 4 miles north

distance from start is √116

Answer 2

Draw a figure.

At his end point the courier is 10 miles east of his starting point and 2 miles south.

He traveled 4 miles north, 10 miles east, and 6 miles south.

The Pythagorean theorem tells you that he is sqrt(104) miles from his starting point.

Note correction to original answer.

The solution is already given: sqrt(104) miles!