It takes Donald 60 minutes to wash a car. How long would it take if he is joined by Joe working 10% faster?
Answer: As the solutions below show, there were several interesting routes to the correct answer, 28.57 minutes. So very well done this time, in order of correct reply, to: John Bowen, consultant, Bromsgrove, UK; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada. Also on the right track, though with a different interpretation, were: Lionel Lesage, CU Valves Dept, KSB Gradignan, Gradignan, France; Dr. Jens Kiesewetter, director applied technology tire & R=rubber: silica & silanes, Evonik Operations GmbH, Smart Materials, Wesseling, Germany. Well done to all above and everyone else who had a go.
Time working together is 28mins 34 secs
[Don's work rate is 1/60 car per munute, ie 0.0166667/min
Joe's work rate is 10% faster, 0.0183333/min
Together, the rate is the sum of these, 0.035/min, so to do 1 car requires 1/0.035 = 28.57 minutes, or 28min 34 sec
Donald and his dude would take 28.57 (29 min. rounding up) minutes to wash a car.
Here is how:
Donald Speed = 1 car / 60 min = 1 car/hr. = t
Dude speed = 1.1 car / 60 m in = 1.1 car/hr.
Donald + dude = 2.1 / 60 min = 2.1 car/hr. = t’
From classical equation speed = Number of cars / time; s = #car / t
As they wash only one car, this become #car = s * t:
Thus, making an equation for both conditions:
(Donald’s) s * t = (Donald+ dude) s’ * t’
Solving for t’ = (s * t)/ s’ = (1 * 60)/2.1 = 28.57 minutes.
If Joe is working 10% faster than Donald, then his output is 11 cars in the time it takes Donald to wash 10.
So Joe takes 60/1.1 = 54.54545454545 minutes to wash a car.
(You might argue 60 minutes minus 10% is 60 - 6 = 54 minutes, but this is not correct, as in 600 minutes, Joe would be able to wash 11.1111.. cars).
So Donald washes 1/60 cars/minute and Joe 1/54.5454545454.. cars/minute. After X minutes working together, X/60 + X/54.5454545454... must = 1.
So X is therefore 1/(1/60 + 1/54.5454545454...) = 1/0.035 = 28.57 minutes.