Question

a man can do certain task in 21 hrs, another can do the task in 28 hrs, and a boy can do the task in 48 hrs.find how long will it take to the task if all work together

Answer 1

work out 1/21 + 1/28 + 1/48 = 1/x

where x is the time required

Answer 2

in one hour first man will do 1/21 of his work
second man 1/28 and a boy 1/48. so all of them will do
1/21 + 1/28 + 1/48 of the total work. Total work is 1/t
so
\[ \frac{ 1 }{ 21}+ \frac{ 1 }{ 28 }+ \frac{ 1 }{48}= \frac{ 1 }{t }\]
solve for t

Answer 3

..so what will be the answer ?

Answer 4

fifcol has explained it better

Answer 5

find the lcm of 21,28,48 and t

and multiply each term by the lcm

Answer 6

wat will be the lcm ?

Answer 7

first find prime factors of each number

21 = 3 * 7
28 = 2 * 2 * 7
48 = 2 * 2 * 2 * 2 * 3

the lcm is the lowest number into which all 3 numbers divide

Answer 8

it means wat

Answer 9

lowest common multiple
for example the lcm of 2 and 3 = 6 (2*3)

the lcm of 6 and 2 = 6 ( not 12):
2 = 2
6 = 2 * 3

there are duplicate 2's so you just take one 2

lcm = 2*3 = 6

Answer 10

or if you don't want to search for lcm you can simply take for lcm the product of denominators e.g.
\[\frac{ 1 }{2 }+\frac{ 1 }{6 }=\frac{ 6 }{ 2*6}+\frac{ 2 }{2*6 }=\frac{ 6+2 }{12 }=\frac{ 8 }{12 }=\frac{ 2 }{3}\]

Answer 11

in case 0f 21, 28 and 48

first take

21 = 3* 7
28 = 2*2* 7

7 is common so lcm = 2*2*3*7

so we have 2 *2*3* 7
and 2*2*2*2*3

2*2 and 3 are common

so lcm = 2 *2*2*2*3*7 = 16*21 = 336

Answer 12

ok so multiply each term by 336t

336t 336t 336t 336
--- + --- + ---- =
21 28 48

16t + 12t + 7t = 336

which is easy to solve

Answer 13

35t = 336
t = 336/35

grab your calculator and work this out