Question 421877
A man walks for 2 hours - on the way there he walks straight at 4/km per hour
 and uphill to the point at 3/km per hour.
On the way back he walks downhill at 6/km per hour and straight at 4/km per hour.
 How many kilometers has he traveled in total after 2 hours?
:
Let f = dist of level ground
Let h = dist of the hill
:
Write a time equation: Time = dist/speed
:
lev time + uphill time + downhill time + lev time = 2 hrs
{{{f/4}}} + {{{h/3}}} + {{{h/6}}} + {{{f/4}}} = 2
combine like terms, use common denominator for the hill times
{{{(2f)/4}}} + {{{(2h)/6}}} + {{{h/6}}} = 2
{{{(2f)/4}}} + {{{(3h)/6}}} = 2
;
Multiply by 12, results
3(2f) + 2(3h) = 12(2)
6f + 6h = 24
:
Simplify, divide by 6
f + h = 4 km is one way distance
therefore
total dist in 2 hrs = 8 km