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Hunter and his workout partner arelifting weights together, doing manysets of each exercise. On a certainexercise, Hunter is using a 19-kilogram bar, increasing the amount ofweight he lifts by 2 kilograms on eachset. His partner, meanwhile, startedout using a 15-kilogram bar and isupping the weight by adding 6kilograms on every set. Eventually,Hunter and his workout partner will belifting the same amount, and will taketurns using the same barbell. Howmany sets will they have completed?How much weight will they be liftingthen?

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sqdancefan

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Answer:

  • 1 set completed
  • 21 kg

Step-by-step explanation:

The difference in mass of the bars is 19-15 = 4 kg. The difference in mass of the added weight is 6-2 = 4 kg. The difference in total mass (bar +added) is reduced by the difference in added mass after each set. The number of sets required to reduce the difference to zero is ...

  (4 kg)/(4 kg/set) = 1 set

After 1 set, Hunter will increase the mass to 19 kg + 2 kg = 21 kg.

After 1 set, his partner will increase the mass to 15 kg +6 kg = 21 kg.

Both will be lifting 21 kg for their 2nd set, after they have completed 1 set.

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Additional comment

You can write equations for the mass being lifted by Hunter (h) and his partner (p) after s sets:

  h = 19 +2s

  p = 15 +6s

The masses will be equal when ...

  h = p

  19 +2s = 15 +6s

  19 = 15 +4s . . . . . . . subtract 2s

  4 = 4s . . . . . . . . . . . subtract 15

Note that the number on the left side of the equation is 19-15, the difference of bar masses. The coefficient on the right side is 6-2, the difference in the added masses. To find the number of sets (s), we divide the equation by the coefficient of s:

  4/4 = s = 1

In the above solution we skipped directly to this final division in order to find the number of sets until the lifted masses were equal.

Answer:

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