Question

One man can do a piece of work in 3 hours ; another can do the same piece of work in 2 hours. how long will they take if they work together?

Answer 1

$\huge \bf \green{ Hey \: there !! }$

→ Given :- 1 man alone can finish the work in ‘3’ hours .

And, other man alone can finish it in ‘2’ hours .

Then, 1 man's 1 hour's work = $\frac{1}{3}$

And, other man's 1 hour's work = $\frac{1}{2}$

▶ Now, A/Q 

→ If both man work together , Then , the 1 hour's work :-

$= \frac{1}{3} + \frac{1}{2} . \\ \\ = \frac{2 + 3}{6} . \\ \\ = \frac{5}{6}.$

✔✔ Hence, no. of hours taken by both work together is 1 hours 12 minutes ✅✅ .

THANKS

#BeBrainly.

Answer 2

Hey dear here is your answer!!!!!

___________________________

Let the two men be named as A and B.

Time take by A to complete a work is 3 hours.

Time take by B to complete a work is 2 hours.

Therefore, efficiency of A would be = $\frac{1}{3}$

And, efficiency of B would be = $\frac{1}{2}$

If they work together their combined efficiency would be:-

$\frac{1}{E}$ =  $\frac{1}{3}$ + $\frac{1}{2}$

$\frac{1}{E}$ = $\frac{2+3}{6}$

$\frac{1}{E}$ = $\frac{5}{6}$

E = $\frac{6}{5}$

Therefore, they would take $\frac{6}{5}$ hours to complete the work together.

$\frac{6}{5}$ hours = 1 hr 12 minutes.

$\large\boxed{\large\boxed{\large\boxed{Solved !}}}}$

❣️⭐ Hope it helps you dear...⭐⭐❣️❣️