Answer:
The values is
Explanation:
From the question we are told that
The speed of the fire engine is
The frequency of the tone is
The speed of sound in air is
The beat frequency is mathematically represented as
Where is the frequency of sound heard by the people in the fire engine and is is mathematically evaluated as
substituting values
Thus
The speed of Matt is 10 mph.
Doug runs 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour. Then Doug’s speed equals x + 2 miles per hour. Each lap is one-quarter of a mile, so Doug runs 1.5 miles in the time it takes Matt to run 1.25 miles.
Rate of Matt is x
Rate of Dough is (x + 2)
Time taken by Matt is 1.25/x
Time taken by Dough is 1.25/(x + 2)
Distance covered by Matt is 1.25
Distance covered by Dough is 1.5
Dough and Matt took the same amount of time from the time Doug started, so make an equation by setting the two times in the chart equal to each other, and then solve for x:
=
1.5x = 1.25(x + 2)
1.5x = 1.25x + 2.5
0.25x = 2.5
x = 10
So Matt ran at 10 miles per hour.
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