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# If Machine X can produce 80 widgets in 4 hours

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If Machine X can produce 80 widgets in 4 hours [#permalink]  27 Aug 2013, 00:27
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If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

A) Machine Y works at 3/4 the speed of machine X
B)If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

OA not provided
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Re: If Machine X can produce 80 widgets in 4 hours [#permalink]  27 Aug 2013, 02:09
Question : Rate of X is given. What is rate of X and Y together i.e What is the rate of Y?

1)Rate of Y can be found. Sufficient.
2)Rate of Y can be found. Sufficient.

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Re: If Machine X can produce 80 widgets in 4 hours [#permalink]  27 Aug 2013, 13:52
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If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?
==> X produces 20 widgets/hour (= 80/4)

A) Machine Y works at 3/4 the speed of machine X
==> Y produces 3/4 x 20 = 15 widgets/hour
==> (X + Y) produce (20 + 15) = 35 widgets/hour
==> to produce 500 widgets, (X+Y) need 500/35 hours
A is sufficient.

B)If Machine Y's speed doubled, it would produce 120 widgets in 4 hours
==> double speed of Y = 2 Y work simultaneously ==> (Y+Y) produce 30 widgets/hour (=120/4)
==> One Y produces 15 widgets/hour
==> (X + Y) produce (20 + 15) = 35 widgets/hour
==> to produce 500 widgets, (X+Y) need 500/35 hours
B is sufficient.

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Re: If Machine X can produce 80 widgets in 4 hours [#permalink]  27 Aug 2013, 22:07
Expert's post
guerrero25 wrote:
If Machine X can produce 80 widgets in 4 hours, how long would it take machine X and Y working together, to produce 500 widgets?

A) Machine Y works at 3/4 the speed of machine X
B)If Machine Y's speed doubled, it would produce 120 widgets in 4 hours

OA not provided

If Machine X can produce 80 widgets in 4 hours, :- Machine X can produce 20 widgets per hour

Lets assume Machine Y can produce a widgets per hour.

how long would it take machine X and Y working together, to produce 500 widgets? :- To Produce 500 widgets, it would take them $$\frac{500}{(20+a)}$$ hours.

So the Question is basically asking us How many widgets can Machine Y produce in one hour OR How many widgets can Machine X and Y, working togetger, produce in one hour.

A) Machine Y works at 3/4 the speed of machine X :- Machine Y can produce $$\frac{3}{4} 20$$ widgets in one hour i.e. 15 widgets per hour - Sufficient.

B)If Machine Y's speed doubled, it would produce 120 widgets in 4 hours :- We know Machine Y can produce a widgets per hour. This statement saying us that, with doubled speed, Machine Y can produce 30 widgets per hour. Hence 2a = 30 -----> a = 15 Sufficient.
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Re: If Machine X can produce 80 widgets in 4 hours   [#permalink] 27 Aug 2013, 22:07
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