Rosyth Sch 2007 PSLE Math Prelim Q40

Machine A can do a printing job in 2 hours. Machine B can do the same job in 3 hours. If both machines are used at the same time, how long would it take to complete half the printing job?

Solution

Since Machine A takes 2 hours and Machine B takes 3 hours, Machine A will be able to get more work done than Machine B, if both are used at the same time, in the ratio of 3:2 as shown below.



(Machine A)
Whole job ----- 2 hours
3/5 of job ----- 3/5 x 2 hours = 6/5 hours

Time taken if both machines are used at the same time is 6/5 hours because while Machine A completes 3/5 of the job, Machine B completes the remaining 2/5 of the job.

Time taken for whole job done if both machines are used at same time is therefore 6/5 hours

Time taken for half the job done if both machines are used at the same time is
1/2 x 6/5 hours = 3/5 hour.

Answer: 3/5 hour