You are biking at a speed of 18 miles per hour. you are 3 miles behind your friend, who is biking at a speed of 12 miles per hour. write and solve an equation to find the amount of time it takes for you to catch up to your friend.

A. solve by logic:

You bike 18 miles per hour, and your friend, 12 miles per hour.

In one hour, you'd catch up 6 miles, so in half-an-hour you'd catch up 3 miles.

B. Solve by equations:

Let x=time needed in hours

18x-12x=3

6x=3

x=3/6=0.5 hours

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: