Work Rate One worker can complete a task in h hours while a second can complete the task in 3h hours. Show that by working together they can complete the task in t = 3/4h hours.

Answer: t = (3/4) h hours.

Therefore, it takes both of them (3/4) h hours to complete the task.

Step-by-step explanation:

Let

t1 represent the time taken for the one worker to complete a task.

t2 represent the time taken for the second worker to complete a task

And t represent the time taken for both.

t1 = h

t2 = 3h

Let x represent the task.

x = rate * time

r1, r2 and r are the rates at which first, second and both worker works

x = r1 (t1) ... 1

x = r2 (t2) ... 2

x = r (t) ... 3

And,

r = r1 + r2. (Rate of both equals sum of rates of the two)

From eqn 1 and 2

r1 = x/t1 = x/h

r2 = x/t2 = x/3h

r = r1 + r2 = x/h + x/3h = 4x/3h

Substituting r = 4x/3h into equation 3

x = r (t)

x = (4x/3h) t

Making t the subject of formula

t = x / (4x/3h)

t = 1 / (4/3h)

t = 3h/4

t = (3/4) h hours.

Therefore, it takes both of them (3/4) h hours to complete the task.