Question

John can can do a job in 2 hours. His friend, Ben, can can do the same job in 6 hours. How long would it take for two of them to do the job together?

PLS HELP WITH EXPLANATION FAST, 20 POINTS

Answer 1

3/2 hours, or 1.5 hours

Explanation:

assume the total job is 1

and assume it took them x hours to take them to do the job

The speed that john can do the job: 2 hours

The speed that ben can do the job: 6 hours

Now the equation:

x/2+x/6=1

3x/6+x/6=1

4x/6=1

4x=6

x=1.5 hours or 3/2 hours

Answer 2

1.5 hours

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.