Question

How do I do this problem?

Answer 1

Answer:

Kate finished the race in 52 seconds

Alexia finished the race in 58 seconds

Trina finished the race in 49 seconds

Step-by-step explanation:

From this work problem we can set up these series of equations:

$k+a+t=159\\a=k+6\\t=k-3$

First we need to create only one variable in the first equation in order to solve it, so we can substitute in the other equations into the first one. That would look like this

$k+(k+6)+(k-3)=159$

Then we can simplify this

$3k +3=159\\3k=156\\k=52$

Now that we solve for Kate's time, we can use the other 2 equations to find the times of Alexia and Trina

Using the equation for Alexia's time and plugging in Kate's time gives us

$a=52+6\\a=58$

Using the equation for Trina's time and plugging in Kate's time give us

$t=52-3\\t=49$