# a radio station’s signal has a radius of a hundred miles

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## a radio station signal has a radius of 100 miles.

if you drive at a constant speed of 40 miles an hour, nonstop, directly across the diameter of the signal, how long can you listen

let

t = the time that the signal can be heard

v = 40 mph the speed

d = the diameter or the signal

the diameter of the signal d = 2*radius

d = 2*100

d = 200 miles

since speed = distance/time => time = distance/speed

t = d/v

so t = 200/40

t = 5 hours

the signal can be heard for 5 hours.

## A radio station’s signal has a radius of 100 miles. If you drive at a constant speed of 40 miles an hour, non stop, directly across the diameter of the signal; how long can you listen to the station before the signal fades?

It’s quite easy to work out how long you can listen to a radio station before the signal fades if you’re travelling at 40 miles an hour across the diameter of the 100-mile radius signal. The best thing to do is break it down!

- The radius of the signal is 100 miles, and since the diameter is double the radius, you’ll be driving 200 miles.
- You’re travelling at 40 miles an hour, so to work this out you can do a simple division sum: 200/40=5. Alternatively, you could count how many 40’s go into 200… The answer is 5!
- So there you have it. You can drive for 5 hours at 40 miles an hour listening to the radio before the signal fades.

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