Troubleshooters.Com Presents

2/1999 Troubleshooting Professional: The Math Behind

Copyright (C) 1998 by Steve Litt. All rights reserved. Materials from guest authors copyrighted by them and licensed for perpetual use to Troubleshooting Professional Magazine. All rights reserved to the copyright holder, except for items specifically marked otherwise (certain free software source code, GNU/GPL, etc.). All material herein provided "As-Is". User assumes all risk and responsibility for any outcome.

# 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