Question

It one machine would take $4$ hours to complete a large production order and another machine $3$ hours to complete the same order. How many hours would both machines take, working simultaneously at their respective constant rates, to complete the order?

• A. $\frac{7}{12}$
• B. $1\frac{1}{2}$
• C. $1\frac{5}{7}$
• D. $3\frac{1}{2}$
• E. $7$

Answer 1

Answer: (C)

$1\frac{5}{7}$

Order completed by machine $M_1$ in 1 hour $=\frac{W}{4}$

Similarly, Order completed by machine $M_2$ in 1 hour $=\frac{W}{3}$

$\Rightarrow \frac{W}{4}+\frac{W}{3}=\frac{7W}{12}$

This means that when both machines are working together work done per hour

$\Rightarrow \frac{W}{\frac{12}{7}}$

So, the work will be completed in $\frac{12}{7}hrs$

as

$\frac{W}{\frac{12}{7}}\times \frac{12}{7}=W$

Therefore Answer is $\frac{12}{7}hrs=1\frac{5}{7}$