Question

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. Identify an equation to find the amount of time t it takes for you to catch up to your friend.

Then solve the equation.

12t-3 = 18t

3 - 12t = 180

18 - 3t = 12

18t - 3 = 120

16

It takes hour(s) to catch your friend.

Answer 1

12t -3 = 18t

Explanation:

Let

d = your friends distance in miles

t = time in hrs

Your equation:

d - 3 = 18t (1)

Because you are 3 miles behind your friend

Your Friend's equation:

d = 12t (2)

To find the amount of time t it takes for you to catch up with your friend,

Substitute (2) into (1)

d - 3 = 18t

12t - 3 = 18t

Equation to find the amount of time t it takes for you to catch up to your friend is 12t - 3 = 18t

Solving the equation

12t - 3 = 18t

Collect like terms

12t - 18t = 3

-6t = 3

t = 3/-6

= -0.5

t = 1/2 hour

Time can not be negative, therefore it will take 1/2 an hour to catch up with your friend