Question

jerry and george are having a hot dog eating contest. jerry can eat 1 hot dog every 30 seconds, and george can eat 3 hot dogs every 80 seconds. at this rate, if neither jerry or george stop eating hot dogs, how many seconds will it be before they eat all 34 hot dogs that elaine prepared for the competition. seconds =

Explanation:

Step1: Calculate Jerry's rate

Jerry eats 1 hot - dog every 30 seconds, so his rate $r_J=\frac{1}{30}$ hot - dogs per second.

Step2: Calculate George's rate

George eats 3 hot - dogs every 80 seconds, so his rate $r_G=\frac{3}{80}$ hot - dogs per second.

Step3: Calculate their combined rate

The combined rate $r = r_J + r_G=\frac{1}{30}+\frac{3}{80}=\frac{8}{240}+\frac{9}{240}=\frac{8 + 9}{240}=\frac{17}{240}$ hot - dogs per second.

Step4: Calculate the time

We know that the number of hot - dogs $n = 34$. Using the formula $t=\frac{n}{r}$, we substitute $n = 34$ and $r=\frac{17}{240}$. Then $t=\frac{34}{\frac{17}{240}}=34\times\frac{240}{17}=480$ seconds.

Answer:

480