Question

Let's practice! You ran around the park once and twice around the field near your house in 10 minutes. At the same speed, you are also able to run around the park three times and twice around the field near your house in 22 minutes. Write down the system of linear equations that represent the statements above

Answer 1

Answer: the time needed to circle one park round is 6 minutes while to circle one round of field takes 2 minutes.

Step-by-step explanation:

Two Variable Linear Equation System

Known :

• Surround the park once and twice around the field near your house in 10 minutes.

• At the same speed, you are also able to run around the park three times and twice around the field near your house in 22 minutes

Asked:

System of linear equations that represent the statements above

Settlement:

For problems like this, we can use the Two Variable Linear Equation System (SPLDV) method. There are 4 ways, 2 of which are elimination which is eliminating one variable, and the other is substitution.

The first step that we do is make the coefficient of one variable the same so that it can be eliminated. We choose the variable x.

We change the word into a variable.

park = t

Field = l

So, the mathematical model of the statement on is known is

t + 2l = 10

3t + 2l = 22

First, we first eliminate one variable, the varaibal that we will eliminate is l.

t + 2l = 10

3t + 2l = 22

----------------- -

-2t = -12

t = -12 / (- 2)

t = 6 minutes

Next, we substitute the value of t into one of the equations.

t + 2l = 10

2l = 10 - 6

2l = 10 - 6

2l = 4

l = 4/2

l = 2 minutes

So, the time needed to circle one park round is 6 minutes while to circle a round of field takes 2 minutes.

Hope it helps ✌

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