Question

Lena and three of her friends bought just enough food so they could go for a 12-day camping trip. Pete and Jane surprised them by showing up at the start of the trip and asking to join, but they brought no food. By what percent would the time for the trip shorten if everyone ate their normal daily portions?

Answer 1

33.3%

Explanation:

The number of people that must be fed has increased from 4 to 6, so is 6/4 = 3/2 as many as planned.

Assuming the additional people eat the food at the same rate as the original people, the time and number of people are assumed to be inversely proportional. That is, the time the food will last is 2/3 of the originally expected time. It has decreased by 1/3 × 100% = 33.3%.

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If you like, you can count rations. For four people for 12 days, at 3 rations per person per day, a total of 144 rations are needed. When the number of people becomes 6, the number of days that will last is ,,,

(144 rations)/(6 persons)/(3 rations/person/day) = 8 days

The percentage change in trip days is ...

(8 -12)/12 × 100% = -4/12 × 100% = -33.3% . . . a decrease of 33.3%