15 machines work at the same rate, 15 machines can complete an order in 8 hours, however 3 of the machines break down after 6 hours. The other machines continue until the order is complete. In total how many hours does EACH machine work? (3 mark question)

When tackling wordy questions such as this the first thing to do is to convert the question into an equation where possible. in this case 15M(Machines) x 8H(Hours)=120MH (Machine Hours). This initial equation indicates to us the number of machine hours required to complete the order. From the second part of the question we find that these 15 machines work for 6 hours continuously without failure leading to 90 Machine Hours on this order (15M x 6H=90MH). However from this point on as 3 Machines break the remaining Machine Hours must be completed by merely 12 of them. The number of Remaining Machine Hours are 30 (120-90=30) which when divided by 12 Machines results in a further 2.5 Hours (30/12= 2.5) required from each machine. Combining the 6 hours previously done by all machines with the further 2.5 hours shows that each of the remaining machines have worked for 8.5 hours. Importantly the presentation of the final answer as 8.5 hours rather than 8 hours 30 minutes is important to receive full marks. Always make sure to look back to the question to see what the units are requested from you to avoid losing simple marks.