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

Distance = velocity x time

Assume the distance moved by your friend is "d" and that the time taken for you to catch to him is "t"

you are moving with a velocity of 18 mph and your friend is moving with a velocity of 12 mph.

distance covered by your friend (d) = 12t miles ... > equation 1

If you add 3 to your rate, your distance will be the same as your friend's. This means that:

d+3 = 18t miles ... > equation 2

Substitute by 1 in 2:

12t + 3 = 18t

3 = 6t

t = 0.5 hours

This means that you will catch up to your friend in half an hour.