heshamelaziry wrote:Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

1/2

2

3

5

6

IMO E
Let me try it.. correct me if I'm wrong

a + b = 1/3 ------------(1)
2a+b = 1/2 -----> b= 1/2 - 2a -------------(2)

Substitute 2 into 1

a + 1/2 - 2a = 1/3
-a = 1/3 - 1/2
-a = - 1/6
a = 1/6 , which means a can produce one widget in 6 hours.

Abdulla wrote:

heshamelaziry wrote:Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

1/2

2

3

5

6

IMO E
Let me try it.. correct me if I'm wrong

a + b = 1/3 ------------(1)
2a+b = 1/2 -----> b= 1/2 - 2a -------------(2)

Substitute 2 into 1

a + 1/2 - 2a = 1/3
-a = 1/3 - 1/2
-a = - 1/6
a = 1/6 , which means a can produce one widget in 6 hours.

Abdulla,

i know that 1/a + 1/b = 1/3, form here I don't understand. I saw different way fo solving it. Yuor seems simpler.

heshamelaziry wrote:

Abdulla wrote:

heshamelaziry wrote:Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

1/2

2

3

5

6

IMO E
Let me try it.. correct me if I'm wrong

a + b = 1/3 ------------(1)
2a+b = 1/2 -----> b= 1/2 - 2a -------------(2)

Substitute 2 into 1

a + 1/2 - 2a = 1/3
-a = 1/3 - 1/2
-a = - 1/6
a = 1/6 , which means a can produce one widget in 6 hours.

Abdulla,

i know that 1/a + 1/b = 1/3, form here I don't understand. I saw different way fo solving it. Yuor seems simpler.

Yeah this is a great formula to use but not with those kind of problems where you have variables instead of numbers (rates).
Usually, I use widget/hour when I have for example, A produce 3 widgets in 4 hours and B produce 2 widgets in 3 hours. In this case your formula works best.

How did you get a + b = 1/3 ? I have usually seen this as either 1/a + 1/b = 1/3 or a + b = 3. I understand you solution, but it is the first time i see work problem solved this way, and like to understand the logic.

heshamelaziry wrote:How did you get a + b = 1/3 ? I have usually seen this as either 1/a + 1/b = 1/3 or a + b = 3. I understand you solution, but it is the first time i see work problem solved this way, and like to understand the logic.

Simply consider the variable as a rate without writing it down as 1/a because at the end you will get a fraction.

if a+b = 1/3, then a and b must be fractions

For this problem, I understood like this:

A+B can produce 1 widget in 3 hours. Therefore, in 1 hour, A+B can produce 1/3 of widget

similarly, 2A+B can produce 1 widget in 2 hours. Hence, 2A+B can produce 1/2 of widget in an hour.

By simplication A = 1/6 . It completes 1/6 th of job . Therefore, it takes 6 hours to do the job alone.

For other types, if A or B value is given, we can determine hourly work rate and try to find the unknown value .

Regards,
Viju