Question 946633
Represent Hannah as H.
Represent Raoul as R.
We can assume that Hannah is a quick woman and is able to travel 6 times as fast Raoul does, we can write it in equation form such as
{{{ H = 6R }}}
Based on the information given, we can create an equation based on how Hannah and Raoul travel together.
{{{ H + R = 63 }}}
Based on the first equation given, we can use the substitution property and substitute H for R, like so the equation is now:
{{{ 6R + R = 63 }}}
Now we can solve the equation to find Raoul's minutes first.
{{{ 6R + R = 63 }}}
{{{ 7R = 63 }}} Combine Like Terms
{{{ 7R/7 = 63/7 }}} Division Property of Equality
{{{ R = 9 }}}

And since we know what R is, we know how many minutes Hannah can travel since Hannah travel 6 times as Raoul.
{{{ H = 6(9) }}}
{{{ H = 54 }}}
Now that we know how many minutes does Hannah travel, we must also show work to imply our values are correct.
{{{ H + R = 63 }}}
{{{ 54 + 9 = 63 }}}
{{{ 63 = 63 }}}