Machines U and T can produce 10,000 units in x hours when working

Question

Machines U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units alone in 4x/3 hours, in terms of x, how many hours will it take T to produce 10,000 units alone?

A. 5x/2 
B. 4x 
C. 2x 
D. x 
E. x/2

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U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x?

Kunal1801 · Answer

I think my answer is correct but my way isn't.
What I did was:
Assume x = 15 (probably a good number)
Therefore together they can complete the work in 15 hours
Let the second machine work rate be x
Now one machine's work rate is (4x)/3 it can do the work in 20 hours
Now 1/20+1/x=1/15
1/x=1/15-1/20
1/x=1/60
Earlier we considered x to be 15 and we got work rate of second machine as 60 
I got my answer as 4x which is 4 times 15= 60 hours of working alone and also it satisfies 1/20+1/60=1/x...

singh.00 · Answer

(Note: I am using K as 1000 to avoid too many digits)

Both combined 10K units in x hrs. Therefore, 10K/x units per hour. --{1}

Now Machine U makes 10K units in 4x/3 hrs. There rate of machine U is 10K/(4x/3) or 30K/4x. --{2}

For Machine T, we could use the above two rates.

Hourly rate of U + Hourly rate of T = Hourly rate combined
(30k/4x) + T = (10k/x)
T = (10k/x) - (30k/4x)
T = (40k - 30k)/4x
T = 10k/4x. or 10000/4x units per hour

Hence, T will take 4x hours to make 10,000 units. Answer is B

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Maheshkv · Answer

rate*time = work done

Here we know that for U: 10k units can be produced in 4x/3 hrs then in x hrs it can produce 10K*(3/4) units which is 7.5k

From information given, the T must have produced remaining 2.5k units when working together with A for x hrs

To produce 10k units T solely requires 2.5k*4 that would be 4x hrs

Lodz697 · Answer

Unit produced by T in x hours = 10.000 / (4x/3) = 7.500 / x

If T produces 2.500 units in x hours, U must have produced 2.500 units in x hours.

Number of needed hours for producing 10.000 units by U = 10.000 / 2.500 = 4 --> final answer 4x

Aboyhasnoname · Answer

U makes 10k in 4x/3 means he makes 3/4 of 10k in x hrs .. means T makes 1/4 of 10k in x hrs ... means for T to make 10k he’d need 4x hours...

Machines U and T can produce 10,000 units in x hours when working

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Machines U and T can produce 10,000 units in x hours when working

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