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].
