Geometric Sequence Problem

[WindowPane01]

Hi, I've got a problem involving geometric sequences. It's more so that I don't understand what it is asking me to do, thankyou.

The question:
James jogs at a speed of 10m/s and Aaron rids a bike at a speed of 15m/s. They have a race with Aaron giving James a head start of 500m.
With the diagram below as a reference (file attached), use Algebra to find the exact distance Aaron will need to cycle to reach James.

My current working out:
So my initial thought is that this is a geometric sequence, where a = 500 and r = 1.5 so I used the formula:
Sn = 500(1-(1.5)^n) / 1-1.5

However, I don't know what to plug in for n and where to substitute the x to find the value.

 

[Deleted member 4993]

Hi, I've got a problem involving geometric sequences. It's more so that I don't understand what it is asking me to do, thankyou.

The question:
James jogs at a speed of 10m/s and Aaron rids a bike at a speed of 15m/s. They have a race with Aaron giving James a head start of 500m.
With the diagram below as a reference (file attached), use Algebra to find the exact distance Aaron will need to cycle to reach James.

My current working out:
So my initial thought is that this is a geometric sequence, where a = 500 and r = 1.5 so I used the formula:
Sn = 500(1-(1.5)^n) / 1-1.5

However, I don't know what to plug in for n and where to substitute the x to find the value.

Why do you think this is a "series" summation problem?

what is the relative speed of A wrt J?

 

[Dr.Peterson]

Hi, I've got a problem involving geometric sequences. It's more so that I don't understand what it is asking me to do, thankyou.

The question:
James jogs at a speed of 10m/s and Aaron rids a bike at a speed of 15m/s. They have a race with Aaron giving James a head start of 500m.
With the diagram below as a reference (file attached), use Algebra to find the exact distance Aaron will need to cycle to reach James.

My current working out:
So my initial thought is that this is a geometric sequence, where a = 500 and r = 1.5 so I used the formula:
Sn = 500(1-(1.5)^n) / 1-1.5

However, I don't know what to plug in for n and where to substitute the x to find the value.

There is no n. There is no sequence or series here.

This is a rate problem. Write an equation that says that after a certain amount of time, they are in the same place.

 

[Steven G]

How far does James jog after t seconds?
How far does Aaron go after t seconds?
What do you do with these results?