Question

john ran \\(\frac{1}{2}\\) mile in 5 minutes, and al ran \\(\frac{1}{3}\\) mile in 4 minutes. which runner ran at a faster rate? question 4 at a certain store, a half - gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. which milk has a che gallon or gallon jug?

Explanation:

First Question (Runner's Rate)

Step1: Calculate John's rate

Rate is distance divided by time. John's distance is $\frac{1}{2}$ mile, time is 5 minutes. So his rate is $\frac{\frac{1}{2}}{5}=\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}=0.1$ miles per minute.

Step2: Calculate Al's rate

Al's distance is $\frac{1}{3}$ mile, time is 4 minutes. His rate is $\frac{\frac{1}{3}}{4}=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}\approx0.0833$ miles per minute.

Step3: Compare the rates

Since $0.1>0.0833$, John's rate is faster.

Step1: Find cost per gallon for half - gallon jug

A half - gallon jug costs $2.95. So a gallon (which is 2 half - gallons) would cost $2.95\times2 = 5.90$.

Step2: Compare with gallon jug cost

The gallon jug costs $5.95. Since $5.90<5.95$, the half - gallon jug (when bought two to make a gallon) is cheaper, so the half - gallon jug has a cheaper cost per gallon.

Answer:

John

Second Question (Milk Cost)