Question 767494
Make a data table.


_____________________speed__________time____________distance
_____________________5______________x______________(___)
_____________________10_____________y______________(___)
TOTAL________________|____________x+y______________35



We want to solve for x and y somehow.  First we could fill in the distance expressions, in case it helps sooner in the process:


_____________________speed__________time____________distance
_____________________5______________x______________(5x)
_____________________10_____________y______________(10y)
TOTAL________________|____________x+y______________35


We must try to do something with the average speed reported of 7 km/hr.
Total distance compared to total time should be this average:
{{{35/(x+y)=7}}}
{{{5/(x+y)=1}}}
{{{x+y=5}}}


We also have a distance equation about total distance traveled:
{{{5x+10y=35}}}
{{{x+2y=7}}}


Solve the system for x and y:
{{{x+y=5}}} and {{{x+2y=7}}}
Subtract first from second.
{{{0+y=7-5}}}
____________________________________________
ANSWER:___________{{{y=2}}} so {{{x=3}}}____________

____________________________________________

ANSWER:   3 hours at 5 km/h and 2 hours at 10 km/h