Respuesta :
The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
time is calculated using the formula
[tex]Time=\frac{Distance}{Speed}[/tex]
In the given question
driver drove 50 miles at slower speed.
Let the slower speed be x miles per hour.
So the time taken to cover 50 miles at slower speed = [tex]\frac{50}{x}[/tex] ...(i)
driver drove 300 miles at faster speed.
given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = [tex]\frac{300}{(x+20)}[/tex]....(ii)
According to the question
the time spent driving at the faster speed was thrice that spent driving at the slower speed.
From equation (i) and (ii) we get
[tex]3*(\frac{50}{x} )=\frac{300}{x+20}[/tex]
[tex]\frac{150}{x} =\frac{300}{x+20}[/tex]
Cross Multiplying we get
[tex]150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20[/tex]
Slower speed = x = 20mph.
Faster speed = (x+20) = 20+20 = 40mph.
Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
Learn more about Speed, Time and Distance here https://brainly.com/question/14975450
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