   SEARCH HOME Math Central Quandaries & Queries  Question from deeqa, a parent: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster, the trip could have been made in 1hr less time. Find the speed 2. The average weekly allowance A of children varies directly as their grade level, G. If the average allowance of an 8th-grade student is $8.56 per week, what is the average weekly allowance of a 5th-grade The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4 working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12 volunteers to complete the job? Hi Deeqa, For your first question look at Stephen's response to an earlier question. The statement that the average weekly allowance A varies directly as the grade G means that there is a constant number k, a number that doesn't change with grade level, so that A = k × G. Since grade 8 students (G = 8) have an average weekly allowance of$8.56 (A = $8.56) you know that$8.56 = k × 8

and hence

k = $8.56/8 =$1.07

Thus A = \$1.07 × G. If G = 5 what is A?

The time T required to do a job varies inversely as the number of people P working means that there is a constant number k so that T = k × 1/P. As I did in the previous problem use the known values to determine k and then apply this value to answer the question.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.