Answer:
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.
