Question

Based on signal strength, a person knows their lost phone is exactly 47 feet from the nearest cell tower. The person is currently standing 23 feet from the same cell tower. What is the closest the phone could be to the person?

Answer 1

Since 47ft is the distance from cell tower it could only be 24ft or 70ft, closest implies the least of the two which is 24ft

Answer 2

Answer:  24 feet

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Explanation:

It might help to draw out a diagram. Refer to the image below. Point A is the cell tower location. Point B is where the person is located. This is a birds eye view. Point B is on the smaller circle of radius 23 ft. The cellphone, which has unknown location, is somewhere on the larger circle of radius 47 ft.

The best case scenario is that the phone is on ray AB, which would make the phone to be 47-23 = 24 ft away from the person. This is the closest the phone could be.

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Extra info:

On the flip side, the worst case scenario is that the phone is on the diametrically opposite side. This would mean the distance from the phone to the person is 47+23 = 70 ft. So the range of possible distances d is $24 \le d \le 70$