Math Question?

Question

Ivan can do a piece of work in 5 hours. After Ivan has worked for 2 hours, Bob joined him and together they completed the job in 2 more hours. How long would it take Bob to do the job alone?

Need to know Bob's rate
And to solve by using this formula
r x t = WD

Answer 1

1- My man Ivan can do it in 5. So he can do 1/5th of it in one hour.
2- Ivan's worked a total of quatro hours' all at the same rate (unless Bob is a girl and Ivan got nervous when she came)
3- Using your equation we can say that the man got 4/5ths of the job done himself (4 times one fifth=rXt=Ivan's WD).
4- WD=1 so Bob must've done 1-(4/5)=1/5th of the job in the two hours he's worked.
5- If Bob can do one fifth in two hours, it will take him 2X5=10 hours to complete 5/5- five fifths, or the entire job by himself (B works at a rate of job per 10 hours, or 1/10).
Don't believe the other fools giving you false answers...

Answer 2

The key to these problems is to always specify the rate in a fraction of the whole job. If it takes Ivan 5 hours to do the job, it means Ivan can do 1/5 of the job in an hour.

So after 2 hours, Ivan has done 2/5 of the job. That leaves 3/5 of the job to do.

Bob can do 1/x of the job in an hour.

Working together, for two hours, they finish the remaining 3/5 of the job:
2(1/5 + 1/x) = 3/5

Multiplying 2 through on the left:
2/5 + 2/x = 3/5

Subtract 2/5 from both sides:
2/x = 1/5

Cross multiply:
x = 10

So Bob takes 10 hours to do the job on his own (or 1/10 of the job every hour).

Answer 3

Let's call the amount of work W. The speed of Ivan is "i". The speed of Bob is "b". Then we get:

5* i = W

2*i + 2(i+b) = W
2i + 2i + 2b = W
4i + 2b = W

comparing it with the first equation:

5i = W
4i + 2b = W

we get:

i = 2b; multiply it by 5
5i = 10b
and,
5i = W

so, W = 10b,

it would take Bob 10 hours to do the job

Answer 4

same as ivan. 5 hours

Answer 5

8 hours