Question

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

Answer 1

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

Lauren will run
`x=80\ \text{ft}` and Clara will run
`40\ \text{ft}`

Explanation:

Velocity of Lauren

`v_l=(24)/(3)\\\Rightarrow v_l=8\ \text{ft/s}`

Velocity of Clara

`v_c=(20)/(5)\\\Rightarrow v_c=4\ \text{ft/s}`

Let distance traveled by Lauren be
`x`

As Clara has a 40 feet head start distance she will travel is
`x-40`

`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`

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

`(x-40)/(4)=(x)/(8)\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=(320)/(4)\\\Rightarrow x=80\ \text{ft}`

Time they will meet is
`(80-40)/(4)=(80)/(8)=10\ \text{s}`.

So, Lauren will run
`x=80\ \text{ft}` and Clara will run
`x-40=80-40=40\ \text{ft}`.