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2/1999 Troubleshooting Professional: The Math Behind

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The Last Mile

Normal repair takes 30 minutes, but 1 in 10 takes 10 hours.

n=number of normal repairs in a 40 hour week
t=number of tough repairs in a 40 hour week
Total repairs = n+t
t = 1/10 * Total repairs
Therefore n=9t   [one in ten is a tough one]

n*.5hours + t*10hours = 40 hours
(9t)*.5 + t*10 = 40
4.5t + 10t = 40
14.5t = 40
t = 40/14.5 = 2.75862068965517241379310344827586
n = 9 * 2.75862068965517241379310344827586 = 24.8275862068965517241379310344828
Total repairs = t + n = 27.5862068965517241379310344827578
Normal repair takes 15 minutes, but 1 in 10 takes 10 hours.

n=number of normal repairs in a 40 hour week
t=number of tough repairs in a 40 hour week
Total repairs = n+t
t = 1/10 * Total repairs
Therefore n=9t   [one in ten is a tough one]

n*.25hours + t*10hours = 40 hours
(9t)*.25 + t*10 = 40
2.25t + 10t = 40
12.25t = 40
t = 40/12.25 = 3.26530612244897959183673469387755
n = 9 * 3.26530612244897959183673469387755 = 29.387755102040816326530612244898
Total repairs = t + n = 32.653061224489795918367346938775
Normal repair takes 30 minutes, but 1 in 10 takes 5 hours.

n=number of normal repairs in a 40 hour week
t=number of tough repairs in a 40 hour week
Total repairs = n+t
t = 1/10 * Total repairs
Therefore n=9t   [one in ten is a tough one]

n*.5hours + t*5hours = 40 hours
(9t)*.5 + t*5 = 40
4.5t + 5t = 40
9.5t = 40
t = 40/9.5 = 4.21052631578947368421052631578947
n = 9 * 4.21052631578947368421052631578947 = 37.8947368421052631578947368421053
Total repairs = t + n = 42.1052631578947368421052631578943