Question

You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.
a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:


b. how long does it take you to jog around the park? it takes you minutes to jog around the park.

Answer 1

Answer:

Part a) The system of equations is

$2x+y=10$

$2x+3y=22$

Part b) The number of minutes it takes you to jog around the park is $6\ min$

Step-by-step explanation:

Part a)  Write a system of linear equations

Let

x-----> the number of minutes it takes you to jog around your block

y---> the number of minutes it takes you to jog around the park

we know that

$2x+y=10$ ----> equation A

$2x+3y=22$ ----> equation B

Part b) How long does it take you to jog around the park?

Multiply equation A by -1 both sides

$-1(*2x+y)=-10$ ------> $-2x-y=-10$ ----> equation C

Adds equation B and equation C

$2x+3y=22\\-2x-y=-10\\-------\\ 3y-y=22-10\\2y=12\\y=6\ minutes$

Find the value of x

$2x+(6)=10$

$2x=10-6$

$x=4/2=2\ minutes$