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Working alone at its constant rate, Machine A can produce 1,050 electrical components in 5 hours. Machine B, working alone, can produce 1,050 electrical components in 15/2 hours. If the two machine work simultaneously for T hours and produce 1,050 electrical components, how many electrical components has Machine B produced at the end of T hours?
- a)140
- b)210
- c)420
- d)525
- e)630
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Working alone at its constant rate, Machine A can produce 1,050 electr...
To solve this problem, let's first find the individual rates of production for each machine.
Machine A produces 1,050 electrical components in 5 hours, so its rate of production is 1,050/5 = 210 components per hour.
Machine B produces 1,050 electrical components in 15/2 hours, which is equivalent to 7.5 hours. Therefore, its rate of production is 1,050/7.5 = 140 components per hour.
Now, let's determine the combined rate of production when both machines work simultaneously for T hours.
Since we want to find the number of electrical components produced by Machine B at the end of T hours, let's assume Machine B works for T hours while Machine A continues to work for 5 hours.
The rate of production for Machine A is 210 components per hour, so in 5 hours it produces 210 * 5 = 1050 components.
Therefore, the combined rate of production for Machines A and B is 210 + 140 = 350 components per hour.
Now, let's find the number of electrical components produced by Machine B at the end of T hours.
Since the combined rate of production is 350 components per hour, in T hours the combined production is 350 * T.
From the question, we know that the combined production is 1,050 components, so we can set up the equation 350 * T = 1,050.
Dividing both sides of the equation by 350, we find T = 3.
Therefore, Machine B has produced 140 components per hour * 3 hours = 420 components at the end of T hours.
Hence, the correct answer is option C) 420.
Machine A produces 1,050 electrical components in 5 hours, so its rate of production is 1,050/5 = 210 components per hour.
Machine B produces 1,050 electrical components in 15/2 hours, which is equivalent to 7.5 hours. Therefore, its rate of production is 1,050/7.5 = 140 components per hour.
Now, let's determine the combined rate of production when both machines work simultaneously for T hours.
Since we want to find the number of electrical components produced by Machine B at the end of T hours, let's assume Machine B works for T hours while Machine A continues to work for 5 hours.
The rate of production for Machine A is 210 components per hour, so in 5 hours it produces 210 * 5 = 1050 components.
Therefore, the combined rate of production for Machines A and B is 210 + 140 = 350 components per hour.
Now, let's find the number of electrical components produced by Machine B at the end of T hours.
Since the combined rate of production is 350 components per hour, in T hours the combined production is 350 * T.
From the question, we know that the combined production is 1,050 components, so we can set up the equation 350 * T = 1,050.
Dividing both sides of the equation by 350, we find T = 3.
Therefore, Machine B has produced 140 components per hour * 3 hours = 420 components at the end of T hours.
Hence, the correct answer is option C) 420.
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Community Answer
Working alone at its constant rate, Machine A can produce 1,050 electr...
Let's calculate the production rates of Machine A and Machine B per hour:
Machine A's production rate = 1,050 components / 5 hours = 210 components per hour Machine B's production rate = 1,050 components / (15/2) hours = 1,050 components / 7.5 hours = 140 components per hour
When Machine A and Machine B work simultaneously for T hours, the total number of components produced is equal to the sum of their individual productions:
Total production = (Machine A's production rate + Machine B's production rate) × T
Substituting the values we calculated earlier:
Total production = (210 + 140) × T = 350 × T
We know that the total production is equal to 1,050 components, so we can solve for T:
350 × T = 1,050 T = 1,050 / 350 T = 3
Therefore, when the machines work simultaneously for 3 hours, Machine B would have produced:
Machine B's production = Machine B's production rate × T = 140 components per hour × 3 hours = 420 components
Hence, Machine B has produced 420 electrical components at the end of T hours. Therefore, the correct answer is (C) 420.
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Working alone at its constant rate, Machine A can produce 1,050 electrical components in 5 hours. Machine B, working alone, can produce 1,050 electrical components in 15/2 hours. If the two machine work simultaneously for T hours and produce 1,050 electrical components, how many electrical components has Machine B produced at the end of T hours?a)140b)210c)420d)525e)630Correct answer is option 'C'. Can you explain this answer?
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