In the same amount of time a new production assembly robot can assembl

Answer must be (D)

R * T = W

Robot's rate: \(\frac{x}{hour} =\\
x\) (time is in hours)
Old assembly line's rate: \(\frac{1}{8}x\)

Time for both: 24 hrs/day * 5 days = 120 hrs

W = R * T
Work done by old: \(\frac{1}{8}x*120 =\\
15x\)
Work done by new: \(x*120 =\\
120x\)

Work completed by both: 15x + 120x = 135x

Answer D

Assign values
This method often makes things easier. Here, maybe not, unless you understand the process (but can't quite get the equations). If robot's rate = 8, answer choices make solving easy.

Let robot's rate = 8 units (per hour), so
Old assembly line rate = 1 unit (per hour)

Both work 24 hours * 5 days = 120 hours

W = R * T
Old line completes (1*120) = 120 units
Robot completes (8*120) = 960 units

Total units: 120 + 960 = 1,020 units

With x = 8, find answer choice that yields 1,080

Immediately eliminate (A) 45x/8 and (C) 135x/8. x=8 "cancels" denominator (results are 45 and 135)

Immediately eliminate (B) 15x, much too small, and (E) 1080x, much too great

Answer (D) 135x, by POE.
Check: 135*8 = 1,080. MATCH

Answer D

If the new robot can assemble x transmissions per hour, the old assembly line can assemble x/8 transmissions per hour.

So the combined rate is x + x/8 = 8x/8 + x/8 = 9x/8,

So in five days, or 24 * 5 = 120 hours, the number of transmissions produced is 9x/8 * 120 = 135x.

Answer: D

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