Question 883509
Uniform Rates for Consumption of Mateiral, food.  
RT=J, where the job is consuming the allotment or some unit of food.  J is for "The job of consuming the allotment of food".


Let r = the consume rate for 1 hiker person.  
If n = number of hikers, then a group of n hikers consumes at the rate of n*r.


The amount of food is related in two equations.


The originally planned group, amount of food being 1:
{{{15*r*8=1}}}; we know this is for 18 people and expect this is the 1 amount of food for 8 days.


The fewer hiker actual group:
{{{12*r*d=1}}}, where d = Days for this group to consume the 1 amount of food.


The amount or allotment of the food is the same for planned and for actual.  That value is 1.


The amount of the food being equal, 
{{{highlight(15r*8=12r*d)}}}.
Solve for d, the number of days.