Algebraic Structures: Solving with Variables

Question

Two athletes are jogging in the same direction along an exercise path. After x minutes the first​ athlete's distance in miles from a parking lot is given by

one seventh x17x

and the second​ athlete's distance is given by

one thirteenth x plus 6113x+6.

​(a) When are the athletes the same distance from the parking​ lot?

​(b) When is the first athlete farther from the parking lot than the​ second?

Answer 1

(1/7)x = x/7

(1/13)x + 6 = x/13 + 6

a.) Set the equations equal to each other. Isolate the variable x.

x/7 = x/13 + 6 ⇒ x/7 - x/13 = 6 ⇒ 13x/91 - 7x/91 = 6 ⇒ 6x/91 = 6 ⇒ 6x = 546 ⇒ x = 91

The athletes will have the same distance from the parking lot after 91 minutes.

b.) Use Desmos graphing calculator to graph these two linear equations. Turns out the second athlete had an early start than the first athlete. After 91 minutes, the first athlete will pass the second athlete because of its speed. 1/7 is greater than 1/13.