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The maximum speed possible on a length of railroad track is directly proportional to the cube root of the amount of money spent ob maintaining the track. Suppose that a maximum speed of 25 km/hr is possible on a stretch for which 450,000 was spend on maintence, find the maximum speed if the amount spent on maintence is increased to $1,750,000 Pls help me show steps please

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boffeemadrid

Answer:

[tex]39.29\ \text{km/h}[/tex]

Step-by-step explanation:

s = Speed of the train

m = Money spent on maintanence

[tex]s\propto m^{\dfrac{1}{3}}[/tex]

Let k be the constant of proportionality so

[tex]s=k (m)^{\dfrac{1}{3}}[/tex]

Now a case is given where 25 km/hr is possible on a stretch for which 450,000 is spent so

s = 25

m = 450000

[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow k=\dfrac{s}{m^{\dfrac{1}{3}}}\\\Rightarrow k=\dfrac{25}{450000^{\dfrac{1}{3}}}\\\Rightarrow k=0.326[/tex]

Now when m = 1750000

[tex]s=k (m)^{\dfrac{1}{3}}\\\Rightarrow s=0.326\times 1750000^{\dfrac{1}{3}}\\\Rightarrow s=39.29\ \text{km/h}[/tex]

The maximum speed of the train would be [tex]39.29\ \text{km/h}[/tex].

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