When a bolt of lightning strikes you don't hear thunder right away. The time in seconds (represented by t) it takes for the thunder to reach your ears is given by t = d over one point zero nine T plus one-thousand fifty d 1.09T + 1050 where d is your distance in feet from the lightning and T is the air temperature in degrees Fahrenheit.

The Empire State Building in New York City is frequently struck by lightning during storms. Suppose you are at Carnegie Hall which is 1.2 miles from the Empire State Building when it is hit by lightning:

1. Write an equation giving the time it takes to hear the thunder as a function of air temperature. (1 mile = 5280 ft)
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t = d over one point zero nine T plus one-thousand fifty 1.2(5280) 1.09T + 1050 = six-thousand three-hundred thirty-six over one point zero nine T plus one-thousand fifty 6336 1.09T + 1050

2. How long would it take to hear the thunder when the temperature is 40ºF?
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It takes about 5.8 seconds until you hear the thunder:
t = six-thousand three-hundred thirty-six over one point zero nine times forty plus one-thousand fifty 6336 1.09(40) + 1050 = six-thousand three-hundred thirty-six over one-thousand ninety-three point six 6336 1093.6 approximately equals⋲ 5.79


3. What was the air temperature if it took 5.6 seconds to hear the thunder?
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The temperature is about 75º F:
5.6 = six-thousand three-hundred and thirty-six over one point zero nine T plus one-thousand fifty 6336 1.09(T) + 1050
6.10T + 5880 = 6336
6.104T = 456
T ⋲ 74.7