Example of work- rate problems, Algebra

An office contains two envelope stuffing machines. Machine A can stuff a batch of envelopes within 5 hours, whereas Machine B can stuff batch of envelopes within 3 hours. How much time it take the two machines working together to stuff a batch of envelopes?

Solution

Let t is the time that it takes both of machines, working together, to stuff batch of envelopes. The word equation for problem is following,

1136_Example of Work- rate problems.png

However we know that the time spent working is t we don't know about the work rate of each machine. In order to get these we'll have to use the initial information given about how much time it takes each machine to do the job independently.  We can employ the following equation to get these rates.

1749_Example of Work- rate problems1.png

Let's begin with Machine A.

1 Job= ( Work Rate of A ) × (5) ⇒     Work Rate of A = 1/5

Now, Machine B.

1 Job = ( Work Rate of B) × (3)   ⇒   Work Rate of B = 1/3

Plugging these quantities in the main equation gives the following equation which we have to solve.

1/5 t +1/3 t = 1                                    Multiplying by 15 through both sides

3t + 5t = 15

8t = 15

t = 15/8 = 1.875 hours

Thus, it looks as it will take two machines, working together, 1.875 hours to stuff batch of envelopes.

Posted Date: 4/6/2013 3:49:43 AM | Location : United States







Related Discussions:- Example of work- rate problems, Assignment Help, Ask Question on Example of work- rate problems, Get Answer, Expert's Help, Example of work- rate problems Discussions

Write discussion on Example of work- rate problems
Your posts are moderated
Related Questions
Multiply 2(b + 5)


write the following function x^2-2x-1 in the form of y=a(x-h)^2+k


The sum of the ages of Dorothy and Dona is 41. In 5 years, Dorothy will be twice as old as Dona. Find their age 3 years ago.

please solve this eqution step by step for me hving trouble -58x-26=8x-230.6

A boy can row a boat at a constant rate of 5 mi/hr in still water, as indicated in the figure. He rows upstream for 18 minutes and then rows downstream, returning to his starting p

find the level of illumination for four fixtures rated at 2800 lumens each if the coefficient of depreciation is 0.75, the coefficient of utilization is 0.6, and the area of the ro

(2/9+4/9)(1/3-5/8)

If P (x) is a polynomial of degree n then P (x) will have accurately n zeroes, some of which might repeat. This fact says that if you list out all the zeroes & listing each one