Thanks to the National Museum Of Mathematics (www.MoMath.org) for providing the following quiz that appeared in the WSJ.
Readers who prefer to use logic instead of math will find this one enjoyable.
click on pictorial to enlargeCar Wash Quiz
Four members of a car washing team have 10 cars to wash and only one hose, which is needed for rinsing but not for washing. Washing a car takes 12 minutes, but the labor can be split up any number of ways (and then the time required is divided by the number of people working together). Rinsing a car takes four minutes.
What is the minimum amount of time the four teammates will need to wash (including rinsing) the 10 cars?
I will post all correct answers or alternatively will send the solution privately to anyone who requests it if no one figures it out.
12 minutes to wash a car - team of 4 which includes rinsing (according to the statement) time needed 120 minutes.
ReplyDeleteTry again but include the divvying up of responsibilities so that the time is less.
DeleteDivvying up the time is not necessary, 3 washing one rinsing behind the 3. Total time 12 min. The 3 are already starting on the next car.
Deleteworking on this for 60 seconds, all the time I can concentrate, came up with 76 minutes. Sounds profitable anyway!
ReplyDelete10 cars, 12 minutes per car, 4 washers sharing job equals 30 min. Per car, only one can rinse, 10 x 4 min. Equals 40 min. Total time 70 minutes. Better? Or wrong?
DeleteThis comment has been removed by the author.
ReplyDelete43 minutes
ReplyDeletePlease provide detail.
Delete4 work on the 1st car - 3 min. each; then 3 work the next 9 cars - 4 min each while 1 rinses 9 cars - 4 min. each car; then 1 rinses 10th car - 4 min.
DeleteBulls-eye. Congrats.
DeleteOfficial answer - Each car requires four minutes to rinse and there’s only one hose. And the fastest any single car can be washed, if all four team members work on it, takes 12/4 = 3 minutes. However, if one teammate is rinsing and the other three are washing, each group takes four minutes to complete a car. So they can work perfectly in parallel, except first there needs to be (at least) one car ready to rinse. That happens fastest if all four students work on it, and then one stays with that car to rinse and the other three start washing the next car. Then just as the rinser finishes the first car, the other three will have finished the second car and the rinsing can continue. In this fashion, the total time needed is 10 × 4 minutes (for all of the rinsing) plus 3 minutes (to prepare the first car for rinsing), or 43 minutes.
I would say 43 minutes. It would take 7 minutes to wash and rinse the first car and then 4 mins to rinse each of the remaining 9 cars . Sevens minutes(first car)... plus 9x4 (the remaining 9 cars)...equals 7 plus 36 equals 43 minutes
ReplyDelete43 minutes?
ReplyDeleteCame up with 44 minutes - used the same logic as HowK so I must have made a math mistake.
ReplyDeleteDoug - here's my answer: 44 mins.
ReplyDeletePlease provide details.
DeleteDoug, Answer I provided was done mentally, but when I sat down with pen and paper, this is what I came up with.
Delete4 men wash the cars twice equals 24 mins.
Next, 2 men wash and 2 men rinse cars equals 12 mins.
Next 4 men rinse 4 cars each time twice equals 6 mins
Total = 24+12+ 6 =42 mins.
Good try but you forgot there is only one hose to rinse.
DeleteI feel you are missing the point in the quiz which states " the hose is needed for rinsing, but not for washing". On that basis, I stand by my solution and it beats yours by a minute.
DeleteThe instructions say “Rinsing a car takes four minutes” so we know that 10 cars being rinsed comes to 40 minutes. I think you second & third steps are not in accordance with this four minute rinsing limitation. Only having one hose points to working with three men on other steps other than washing the first car which sets up the parallel wash-rinse operation.
DeleteI'll say 40 min - I guess I used logic because I thought it would take 36 min to wash all the cars and 4 min to rinse the last car.
ReplyDeleteYou missed washing the first car in three minutes.
Delete