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How long will it take l to catch up to c lauren can run 24 feet in 3 seconds clara can run 20 feet in 5 seconds clara has a 40 foot head start l will catch c in how many seconds after running how many feet

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boffeemadrid

Answer:

They both will meet each other when they both have been running for 10 seconds

Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]40\ \text{ft}[/tex]

Step-by-step explanation:

Velocity of Lauren

[tex]v_l=\dfrac{24}{3}\\\Rightarrow v_l=8\ \text{ft/s}[/tex]

Velocity of Clara

[tex]v_c=\dfrac{20}{5}\\\Rightarrow v_c=4\ \text{ft/s}[/tex]

Let distance traveled by Lauren be [tex]x[/tex]

As Clara has a 40 feet head start distance she will travel is [tex]x-40[/tex]

[tex]\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

The time that will have passed when they both will meet will be the same for both of them so

[tex]\dfrac{x-40}{4}=\dfrac{x}{8}\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=\dfrac{320}{4}\\\Rightarrow x=80\ \text{ft}[/tex]

Time they will meet is [tex]\dfrac{80-40}{4}=\dfrac{80}{8}=10\ \text{s}[/tex].

So, Lauren will run [tex]x=80\ \text{ft}[/tex] and Clara will run [tex]x-40=80-40=40\ \text{ft}[/tex].

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