MAth problem again?

Question

mary takes 3 h to complete a task. Mary and Jim together take 2 h to complete the same tasx. How long will it take KIm to complete thr task working alone?

Answer 1

Mary need 3 hours complete task

Mary effort = task / 3 hours

Mary and Jim need 2 hours complete task.

Mary effort + Jim effort = task / 2 hours
task / 3 hours + task / x hours = task / 2 hours
1/3 + 1/x = 1/2
(x + 3)/3x = 1/2
2(x + 3) = 3x
x = 6

So, Jim need 6 hours to complete task

Answer 2

I haven't done this type of question in a while but I think it's like this:

Mary takes 3 hours at a speed of x to complete the task:
time*speed=1 job
3x=1
so x=1/3

Mary and Jim working together take 2 hours to complete the same task:
2(x+y)=1

Plug in Mary's speed (x=1/3) and you should get that Jim's speed is 1/6:
2[(1/3)+y]=1
2/3+2y=1
2y=1/3
y=1/6

If you plug y into (y)(t)=1
you should get that t (time) is 6 hours for Jim to do the job alone.

Hope that made sense. ^^

Answer 3

Let rate of Mary be x and of Jim be y

So, 3x = 2x + 2y

or 2y = x

So, Jim works half as fast as Mary.

Thus it will take him 6 hours to do the job.

Answer 4

[disclaimer: "t" refers to "task", not "time" ... sorry]
it was slopppy notation, bbut it's understandable


m = mary-speed
j = jimspeed
t = tasklength

(m + J) * 2 = t
m * 3 = t

ques:
jx = t .. solve for "x"


since
m * 3 = t
m = t/3

(m + J) * 2 = t
(t/3 + J) * 2 = t
2t/3 + 2j = t
2j = t/3
j = t/6

since:
jx = t
t/6 * x = t
x = t/(t/6) = 6

meaning that it would take Jim 6 hours by himself

Answer 5

Impossible to answer. There is always some overhead when people are workeing together, you dont specify that overhead . Does Jim have to explain things to Marry ? if so Jim might be ablel to do the Job in less than one hour !