Answer:
1.5 hours
Step-by-step explanation:
Let the work be represented by x for simplification
For john
amount of work done in 2 hours = x
amount of work done by John 1 hours = x/2
For Ben
amount of work done in 6 hours = x
amount of work done by Ben in 1 hours = x/6
when John and Ben works together
amount of work by both of them in 1 hour = amount of work done by John 1 hours + amount of work done by Ben in 1 hours
amount of work by both of them in 1 hour = x/2 + x/6
taking 6 as LCM of 2 and 6
amount of work by both of them in 1 hour = (3x+x)/6 = 4x/6 = 2x/3
Thus,
2x/3 work is done by both of them together in time = 1 hour
to find time taken to do total work which is represented by x
we divide both side by 2/3
2x/3 work is done by both of them together in time = 1 hour
2x/3/(2/3) work is done by both of them together in time = 1/(2/3) hour
on LHS 2/3 in numerator and denominator gets cancelled
on RHS 1/(2/3) = 3/2
x work is done by both of them together in time = 3/2 hours = 1.5 hours
Thus, it will take 1.5 hours for two of them to do the job together.
