[Pri20150522RPRW] More Hands make Light Work?

Question

Introduction

     The key to solving this is to find the total rate of work for Ahmad, Kumar and Calvin.  There is a relationship Work = Rate ´ Time, similar to the relationship Distance = Speed ´ Time, and you can use a similar triangle mnemonic for it.  For example if you cover ‘R’ with your finger, you get the relation Rate = Work / Time.  To organise your information, you may use a table to tabulate the given data.

     Do you believe “more hands make light work”?  Or is it “too many cooks spoil the broth”?  In real life, people may not work harmoniously together, or work at the same rate (never getting tired).  They may get distracted by Facebook, mobile phones or office gossip.  In school mathematics problems, we assume that when people work together, we can just add up their rates of work.  Yes, it is quite funny, but let us just assume.

Solution

Ans: 10 days

Commentary

     When we add up the given rates, we get  ¹/₅,  which is the rate that 2 Ahmads, 2 Kumars and 2 Calvins would work.  Unfortunately we do not have the clones.  We just have one Ahmad, one Kuman and one Calvin.  So we divide that by 2 to get  ¹/₁₀  and this is their combined rate.  This means that they can complete  1  house in  10 days.

     It is possble to do this question without the table, for example by taking the LCM of the denominators and considering how many houses can the guys build in  60  days.  However, the table is a good way of organising information and you can solve the problem by considering the total rate.

HeuristicsUsed

H02. Use a diagram / model   (including table)

H03. Make a systematic list

H05. Work backwards

H09. Restate the problem in another way

H11. Solve part of the problem

Suitable Levels

* Primary School Mathematics

* other syllabuses that involve fractions and ratios