Juan's weight is twice the weight of his little sister Anna. They climb the same set of stairs and find they have the same power. Explain how this can be possible?

We can define power as:

P = W/t

where W is work, and t is time.

And the work needed to climb a distance (we can assume that climb a set of stairs is equivalent to climbing a given height) is:

W = g*h*m

Where:

g = gravitational acceleration

h = height climbed

m = mass.

g and h are the same for Juan and his sister, and the only thing that changes is the mass

The work for Juan is:

Wj = g*h*M

And for his sister, that has half his

Wa = g*h*M/2.

Then the power for Juan, is:

Pj = Wj/t1 = (g*h*M)/t1

Where t1 is the time that Juan needs to climb the stairs.

And for Anna is:

Pa = Wa/t2 = (g*h*M/2)/t2

Where t2 is the time that Anna needs to climb the stairs:

We know that they have the same power, then:

Pj = Pa

(g*h*M)/t1 = (g*h*M/2)/t2

M/t1 = M/2*t2

t1 = 2*t2

This means that the time in which Juan climbs the stairs is twice the time that Anna needs to climb the stairs.

carla slowed down in the beginning of her trip, stopped, and then sped up