Question

The equation $y+4x=100$y+4x=100​ represents your distance y (in meters) from the finish line x seconds after you begin your leg of a relay race. The equation $y+3.7x=94$y+3.7x=94​ represents your opponent's distance from the finish line. How far do you need to run to catch up with your opponent?

Answer 1

Given:

Your distance y (in meters) from the finish line x seconds after you begin your leg of a relay race is

`y+4x=100`

Opponent's distance is

`y+3.7x+94`

To find:

The distance you need to run to catch up with your opponent.

Solution:

We have,

`y+4x=100` ...(i)

`y+3.7x+94` ...(ii)

Subtract (ii) from (i), we get

`y+4x-y-3.7x=100-94`

`0.3x=6`

Divide both sides by 0.3.

`x=(6)/(0.3)`

`x=20`

Put x=20 in (i).

`y+4(20)=100`

`y+80=100`

`y=100-80`

`y=20`

They will meet at (20,20). It means at 20 meters from the finish line after 20 seconds from the beginning.

Put x=0 in (i), we get

`y+4(0)=100`

`y=100`

It means, initially the total distance you and finish line is 100 meters.

You will catch your opponent 20 meter from the finish line. So,

`100-20=80`

Therefore, you need to run 80 meters to catch up with your opponent.