Question 666179
My sister can walk from school to home in 40 minutes.
 I can walk from school to home in 30 minutes.
 Today I stayed for some extra help, and my sister was already 2/5 of the way home when I started.
 If I walk at my usual speed, can I catch my sister before she gets home?
 If "yes" exactly what fraction of the trip have we covered when I catch her?
 If "no" exactly what fraction of the trip have I covered when my sister gets home?
:
Let d = distance from home to school
then
{{{d/30}}} = .033d, your speed walking home
and
{{{d/40}}} = .025d, sister's speed walking home
:
When you start, sister is 2/5 the way which means:
 she has {{{3/5}}}d  or .6d to go 
:
Find her time to get home: {{{(.6d)/.025d}}} = 24 min to get home
then
We know it takes you 30 min to get home so she will beat you home by 6 min
and
You will have covered {{{24/30}}} = {{{4/5}}} of the way home then