Question

The table shows the rates at which Ajay and Tory are biking along the same trail.

Person: Rate:
Ajay: 200
Tory: 250

a. Suppose Ajay began the trail 325 meters ahead of Tory. Write a system of equations to represent the distance y each person will travel after any number of mimutes x.

Answer 1

The rates are:

Ajay : 200

Tory : 250

I assume those are in meters per minute.

Now, we suppose that Ajay began the trail 325 meters ahead, so if we put the zero in Tory position, we got:

Ajay position = 325 meters + 200*x meters

Tory position = 250*x meters

Where x is the number of minutes after they started to bike.

From this, we can compare their positions, and see in which minute x Tory position and Ajay position are the same.

325 + 200x = 250x

325 = 250x - 200x = 50x

x = 325/50 = 6.5 minutes.

So before of x = 6.5 minutes, Ajay is ahead. After x =6,5 minutes, Tory is ahead.

Answer 2

For Ajay ,
`y=200x+325`

For Tory,
`y=250x`

Explanation:

Formula to find distance = rate × time

Rate of Ajay = 200

Rate of Tory = 250

In x minutes

Distance travelled by Ajay = 200 ×x = 200x

Distance travelled by Tory = 250 ×x = 250x

But Ajay was already ahead by 350 meters.

So for Ajay, the distance y traveled in x minutes

`y=200x+375`

For Tory

`y=250x`