Question

The question is two friends race The first friend gets a head start and runs at a steady rate of 0.20 miles per minute The second friend waits one minute and then runs at a steady rate of 0.25 miles per minute how long will it take for the second runner to catch up to the first but my question is what would be the equation cuz that's the thing I'm struggling on.

Answer 1

Let y represent the distance that each friend has traveled, and x represent the time. For convenience, set x=0 at the moment that the second friend starts to run.

Now, state an equation for the position of each friend. Since the first one has been runing for a minute, it's position when x=0 is:

`(0.20\text{ miles per minute})(1\text{ minute})=0.20\text{ miles}`

Since the rate of change of the position with respect to time is 0.20, then it can be identified as the slope of a line:

`y=0.20+0.20x`

For the second friend, since it stats at y=0 when x=0, and his rate of change is 0.25, then:

`y=0.25x`

To find the moment when both friends meet, replace y=0.25x in the first equation:

`0.25x=0.20+0.20x`