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It would take one machine $4$ hours to complete a production order and another machine $2$ hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.

1. $2/3$
2. $3/4$
3. $4/3$
4. $7/3$

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Migrated from GO Electronics 7 months ago by Arjun

+1 vote
Machine $A$ takes $4$ hours and machine $B$ takes $2$ hours to complete the work.
$\text{Efficiency}=\dfrac{\text{Work}}{\text{Time}}$

Let the amount of work be $X.$

Efficiency of $A=\frac{X}{4}$
Efficiency of $B=\frac{X}{2}$

If both machines work simultaneously at their respective constant rates, then

Effective Efficiency $=$ Efficiency of $A$ $+$ Efficiency of $B=\frac{X}{4}+\frac{X}{2} = \frac{3X}{4}$

Effective Time$=\dfrac{X}{\frac{3X}{4}}=\dfrac{4}{3}$ hours.

So, the correct answer is $(C).$
by Veteran (59.4k points)
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Let the production order be 8 items(any multiple of L.c.m(2,4) like 4,8,12,16... would work).

Since 1 st machine completes the order in 4 hours, it is producing at a rate of 2 units per hour.

Similarly 2 nd machine produces at a rate of 4 units per hour.

If both machines are working simultaneously, together they produce 6 units per hour.

$\therefore$ 8 units are produced in $8/6$ hours.

option c is the answer

by Active (4.6k points)