SOLUTION: For a hike the guide packed sufficient food to last 8days for 15 people. If three did not show and with the same rate of consumption, how many days would the food last for the 12

Algebra ->  Rate-of-work-word-problems -> SOLUTION: For a hike the guide packed sufficient food to last 8days for 15 people. If three did not show and with the same rate of consumption, how many days would the food last for the 12       Log On


   

Question 883509: For a hike the guide packed sufficient food to last 8days for 15 people. If three did not show and with the same rate of consumption, how many days would the food last for the 12 people
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Ar%2A8=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%2Ar%2Ad=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%2815r%2A8=12r%2Ad%29.
Solve for d, the number of days.