Question

Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?A. 25%B. 3313%C. 50%D. 6623%E. 75%

Answer 1

Answer:

$66\dfrac{2}{3}\%$

Step-by-step explanation:

Given,

The number of cartons = k,

Time taken by machine a = 8 hours,

So, the number of cartons made by machine a in one hour

= $\frac{\text{Cartons in 8 hours}}{8}$

= $\frac{k}{8}$

Time taken by machine b = 4 hours ,

So, the number of cartons made by machine b in one hour

= $\frac{k}{4}$

Total cartons made in 1 hour = $\frac{k}{8}+\frac{k}{4}$

$=\frac{k+2k}{8}$

$=\frac{3k}{8}$

∵ for the whole number value of k,

$\frac{k}{4}>\frac{k}{8}$

i.e.  machine b is faster,

Also, the percent of the cartons were sealed by the machine b

$=\frac{\text{Cartons made in 1 hour by machine b}}{\text{Total cartons}}\times 100$

$=\frac{\frac{k}{4}}{\frac{3k}{8}}\times 100$

$=\frac{2}{3}\times 100$

$=\frac{200}{3}$

$=66\dfrac{2}{3}\%$

Hence, OPTION D is correct.