Let ${ t }_{ 1 }$ and ${ t }_{ 2 }$ be the time that Renata and Fernanda, respectively, need to complete the trip. And $x$ the number of visible steps.
Considering Renata's trip and knowing that ${ v }_{ r }=3{ v }_{ f }$
$3v_{ f }-v_{ e }=\frac { x }{ t_{ 1 } } \\ v_{ f }=\frac { 150 }{ { t }_{ 1 } }$
Dividing the first equation by the second, we find:
$x=\frac { 50(3v_{ f }-v_{ e }) }{ v_{ f } } (I)$
Now, considering Fernanda's trip:
$v_{ f }+v_{ e }=\frac { x }{ { t }_{ 2 } } \\ v_{ f }=\frac { 75 }{ t_{ 2 } }$
Dividing the first equation by the second, we find:
$x=\frac { 75(v_{ f }+v_{ e }) }{ v_{ f } } (II)$
And we have:
$(I)=(II)→50(3v_{ f }-v_{ e })=75(v_{ f }+v_{ e })→\frac { v_{ e } }{ v_{ f } } =\frac { 3 }{ 5 } (III)$
Now, using (III) in (II):
$x=75\left( 1+\frac { v_{ e } }{ v_{ f } } \right) =75\left( 1+\frac { 3 }{ 5 } \right) =120$