Problem Solving

Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

Answer: By calculation, we find out that Machine A produces 3 bolts/sec, and Machine B produces 5 bolt/sec.

To find out how much they produce simultaneously, GMAT assumed that based on above, they make 8 bolts/sec, hence can find out how many sec it will take them to produce 200.

My question is, why did we not use the formula: 1/3 + 1/5 =1/T to find how much total they produce in 1 sec?

Any help appreciated!

1/3 + 1/5 = 1/T is used when we know that 1 bolt can be made in 3 sec by A and in 5 sec by B and thus in T sec (combined)
A 1 bolt: 1/3 sec
B 1 bolt: 1/5 sec
Thus time taken combined for 1 bolt = T
1/T = 1/(1/3) + 1/ (1/5) = 8
This T = 1/8. 1 bolt can be made in 1/8 sec or in 1 sec we can make 8 bolts...

cans wrote:1/3 + 1/5 = 1/T is used when we know that 1 bolt can be made in 3 sec by A and in 5 sec by B and thus in T sec (combined)
A 1 bolt: 1/3 sec
B 1 bolt: 1/5 sec
Thus time taken combined for 1 bolt = T
1/T = 1/(1/3) + 1/ (1/5) = 8
This T = 1/8. 1 bolt can be made in 1/8 sec or in 1 sec we can make 8 bolts...

A simpler way to look at it maybe that in this case you already know the rate of work done per unit time which is 3 and 5 resp for the 2 machines. In cases, where we cannot quantify the work in terms of units directly, for example a building or a dam etc, we can use the fraction method as rightly pointed out by you.

Thouraya wrote:Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

Answer: By calculation, we find out that Machine A produces 3 bolts/sec, and Machine B produces 5 bolt/sec.

To find out how much they produce simultaneously, GMAT assumed that based on above, they make 8 bolts/sec, hence can find out how many sec it will take them to produce 200.

My question is, why did we not use the formula: 1/3 + 1/5 =1/T to find how much total they produce in 1 sec?

Any help appreciated!

Machine A produces bolts at a uniform rate of 120 every 40 seconds , so it produces 3 bolts/sec

Machine B produces bolts at a uniform rate of 100 every 20 seconds , so it produces 5 bolts/sec


Together they produces 8 bolts/sec




Now to produce 200 bolts time required is 200/8 => 25 seconds...[/b]

how u calculated both together can produce 8 bolts per second??????

machine A: 120/40= 3 bolts/sec
machine B) 100/20=5 bolts/sec
together in one second : 1/3+1/5= 8/15 ==> each second 15/8 bolt can be produced
now 200 bolts in ?? seconds
200*8/15= 320/3

where i did wrong here?????????

mehrasa wrote:how u calculated both together can produce 8 bolts per second??????

machine A: 120/40= 3 bolts/sec
machine B) 100/20=5 bolts/sec
together in one second : 1/3+1/5= 8/15 ==> each second 15/8 bolt can be produced
now 200 bolts in ?? seconds
200*8/15= 320/3

where i did wrong here?????????

Bro I am using the simple concept of addition of efficiency of Machine A and B...

I am deliberately not using fractions beacuse it is time consuming.


If A can produce 3 units/ sec and B can produce 5 units / sec , then total they produce 5 + 3 = 8 units/second.

This 8 units is the combined production of Machine A and Machine B working Individually and Individually , in a second....


Consider U hav 2 machines in your factory and U run them for a second each:


A producing 3 units

B producing 5 units
____________________

Total 8 units


So Working Independently they produce 8 units / second...





Now consider this as a problem of Time , Speed and Distance...


Here Ur distance is 200 units and Speed is 8 units / sec


So , Tie taken for Production of 200units is 200/8 { Using simple concept , Time = distance/Speed}

Thus total time taken is 25 seconds...


Hope this clears your doubts..

Thouraya wrote:Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

Answer: By calculation, we find out that Machine A produces 3 bolts/sec, and Machine B produces 5 bolt/sec.

To find out how much they produce simultaneously, GMAT assumed that based on above, they make 8 bolts/sec, hence can find out how many sec it will take them to produce 200.

My question is, why did we not use the formula: 1/3 + 1/5 =1/T to find how much total they produce in 1 sec?

Any help appreciated!

We don't have to because we are already given the respective rates
A's rate 120 bolts every 40 sec or 3 bolts/sec
B's rate 100 bolts every 20 sec or 5 bolts/sec
So you just add them up

You would use the combined rate when they've given you the number of hours each machine has
taken to complete a task

I've used the working problem equation: 1/A + 1/B = 1/T

Inserted as follows:
100/20s + 120/40s = 200/x
Search for x
320/40s = 200/x
x= 25s.

Thouraya wrote:Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?

Answer: By calculation, we find out that Machine A produces 3 bolts/sec, and Machine B produces 5 bolt/sec.

[/b]

Efficiency of machine A is - 3 bolts/sec

Efficiency of machine B is - 5 units/sec


Togather they produce 8 bolts/sec


Time taken to produce 200 bolts is 200/8 = 100/4 => 25 seconds...