job efficiency

John’s neighbor, Mrs. Lee, will pay John $360.00 when John finishes planting the flowers in her garden  within certain number of days. John has worked for 6 days but has only planted 1/3 of all the flowers. He knows that if he does not finish the job on time, he will not get paid the full amount so he asked Peter to help him. It took Peter and John only 1 day to finish the rest of the job . 

Mrs. Lee paid them $360.00. John and Peter were very happy until they began to divide the money between them. 

John said:” I have worked for altogether 7 days but you have worked for only 1 day. Therefore, the total number of days on the job was 8 and we need to divide 8 into $360 to see how much each of us should be paid per day. ” So John did:

360÷8=$45.00

John said:” Peter, you worked for only one day, so you should get $45.00. I worked for 7 days, so the amount I should get is : 45 x 7=$315.00″

Peter said:” No, You have said that we should be paid according to the amount of work each person did. The first 1/3 of the job was done by you, so you should get: 360 x 1/3=$120.00 from that. The rest of the job was done by both of us so each one of us should get (360-120) ÷ 2=$120.00 from 2/3 of the job. Therefore, you should get altogether 120+120=$240.00.”

John did not agree with Peter so they kept arguing until they saw Mr. Smith, a wise man and a person that they both trust. They presented the problem to Mr. Smith. Mr. Smith thought for a while and said:” Peter should get $240; John should get $120.” 

” Why?” they both asked. 

Mr. Smith said:” John did 1/3 of the job in 6 day so on the average,  in one day,he finished 1/3 + 6=1/18 of the job therefore he should be paid 360 x 1/18=$20 per day. He has worked for 7 days he should get 20 x 7=$140; Peter should get the rest of the money which is 360-140=$220.”

He looked at both of them and said:” People are paid not only by the amount of time they spend on a job by also  by their job efficiency (how fast the job is done) .”

If you need to set a solid foundation for word problems, please get word problems: detailed explanations of reasoning and solving strategies: Volume 11-A, 11-B and 12. and if you have any questions about the problems in the books, we can talk about them in the blog.