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Tunteg · Mar 17, 2011, 06:51 AM

If A&B work together they will finish the job in 2 hours and 48 minutes. If they work independently; A will finish the job 4 hours and 12 minutes before B. The challenge is to find both their individual rate/speed for finishing the job if they work independently. Just to clarify (my English might a little un-clear), the A will do the job in X hours if he works alone; and B will finish the job in Y hours if he does it only by himself. ^^

Cheers & kudo for anyone who can solve this problem (and of course explain to me =)

ebaines · Mar 17, 2011, 08:01 AM

Here's how to think it through - use the analogy of distance = rate time time. Suppose the job is to travel distance D. For worker A who takes time T_a to do his job his velocity is:
$ V_a = \frac D {T_a} $

And for worker B you have

$ V_b = \frac D {T_b} $

When they work together the time required is

$ T_{total} = \frac D {V_{total}} $

Note that for all three equations D is a constant - it's the size of the job and is the same for both workers. When they work together their combined velocity is

$ V_{total} = V_a + V_b $

So you have:

$ T_{total} \ = \ \frac D {V_{total}}\ =\ \frac D {V_a + V_b} \ = \ \frac D {\frac D {T_a} + \frac D {T_b}}\ = \ \frac 1 {\frac 1 {T_a} + \frac 1 {T_b}} $

For your problem you've been given $T_{total}$ and the value for $T_a - T_b$ . So you can now solve for $T_a$ and $T_b$ . Post back and show us what you get for an answer.

gdfgtt · Apr 1, 2011, 06:23 PM

its saying that if they work together they would finish faster if they work independently it would take them 2 hours more.so worker b you have Vb = D-T b
for a you have D-T a.so Va+Vb= . D v total