# 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!

1. The radius of the signal is 100 miles, and since the diameter is double the radius, you’ll be driving 200 miles.
2. 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!
3. 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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