Roger can run one mile in 18 minutes. jeff can run one mile in 15 minutes. if jeff gives roger a 1 minute head start, how long will it take before jeff catches up to roger?

Alright, lets get started.

Roger can run one mile in 18 minutes.

Jeff can run one mile in 15 minutes.

Suppose in x minutes, they both will catch up.

Roger runs in 18 minutes = 1 mile

So, Roger will run in 1 minute = miles

So, Roger will run in x minutes = miles

Jeff runs in 15 minues = 1 mile

So, Jeff will run in 1 minute = mile

As Jeff gives roger a 1 minute head start, means Jeff will have x-1 minute time to run

So, Jeff will run in (x-1) minute =

As both are cathing up means they both runs same distance, means

Cross Multiplying

x = 6 minutes

So for calculating distance =

Distance = miles

It means it will take 1/3 or 0.33 miles before jeff catches up to roger.   :   Answer

Hope it will help :)

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: