Acceleration: guy and a student are competing against each other

[Julia Maria]

Homework Statement

A guy and a student are competing against each other in a 100m long race. The guy start before the student. When the guy is halfway the student start running. They are finishing at the same time. We assume that at any time we can talk about their speed.

Show that you and the guy have exactly the same rate of at least one time point after the boy started to run.
How much information do you need to complete the task?

Homework Equations

S`(t) = G`(t)

The Attempt at a Solution

Since the guy started before the student. The student has to run twice as fast to finish at the same time. So his acceleration has to pass the guy acceleration at one time. ( Imagine a graph.
and when they finish at the start line.
They also have the same speed when they both start, but they do not start at the same time. So it is not valid since its not at the same time.

So how can I show this and when do they have the same speed. Am I on the right track?

 

[SammyS]

Homework Statement

A guy and a student are competing against each other in a 100m long race. The guy start before the student. When the guy is halfway the student start running. They are finishing at the same time. We assume that at any time we can talk about their speed.

Show that you and the guy have exactly the same rate of at least one time point after the boy started to run.
How much information do you need to complete the task?

Homework Equations

S`(t) = G`(t)

The Attempt at a Solution

Since the guy started before the student. The student has to run twice as fast to finish at the same time. So his acceleration has to pass the guy acceleration at one time. ( Imagine a graph.
and when they finish at the start line.
They also have the same speed when they both start, but they do not start at the same time. So it is not valid since its not at the same time.

So how can I show this and when do they have the same speed. Am I on the right track?

Hello Julia Maria. Welcome to PF!

The guy travels 50m in the same time that the student 100m. How do their average velocities compare over this time interval?

 

[Julia Maria]

Average velocity is the rate of change of displacement with time.
Δr=50m
v=Δr/Δt Average velocity for the boy
v=(2*Δr)/Δt For the student

So the students average velocity. is twice the boys.

So how do I show when they have the same rate?
And Î`m missing the time to complete the task?