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.
