## Al and Fred’s Car Wash

Al washes a car in 6 minutes. Fred washes the same car in 8 minutes. How long will it take them to wash the car together?

There isn’t enough information, thus there’s no one, right answer. (As frustrating as that may be)

This is from the TV show Boy Meets World, season 1 episode 12.

Posted in Brain Teasers

6 Comments on "Al and Fred’s Car Wash"

Karel D says
February 17, 2019 @ 15:44

Is there really no right answer to this? I can imagine the following reasoning: Imagin that AI and Fred wash a car together, each starting from a different side of a car. In 3 min AI will have washed his half of the car and Fred will have washed 3/4 of his half of the car. So they cannot wash it in less than 3 minutes. On the other hand, they will definitely be done in 4 minutes, since for the Fred it takes 4 minutes to wash half of the car and AI is faster than Fred. By now we have at least lower and upper bound [3,4]min for them.
To solve it exactly, we can do as follows: in 6*8=48 min they will wash 6+8=14 cars in separate. From that, we can get that it takes 48/14 = 3.42 min for them to wash one car (which is within the [3,4] bounds).

However, if the impossibility of the answer to this solution lies in the fact, that we know how long it takes for them to wash the whole car and not a part of the car, then okay, but personally, I don’t like this answer.

Mark W says
February 24, 2019 @ 01:21

I’m with Karel D, but arrived at a different answer:

If they both took 6 mins. & teamed up, it should take them 3 mins.
If they both took 8 mins. & teamed up, it should take them 4 mins.

If one takes 6, the other 8 & they team up( same as if they take 7 mins. each ), then we arrive at 3.5 mins.?

Ramon says
March 1, 2019 @ 00:30

Why’s it so complicated? Person A washes 1/x of the car in one minute. Person B washes 1/y of the car in one minute. Together, in one minute, they wash (1/x + 1/y) of the car. Invert to find how long they take.

Rose says
April 5, 2019 @ 12:42

Al washes 1/6 of the car in a minute. Fred washes 1/8 in a minute. Together, they would wash 1/6 + 1/8 = 7/24 of the car in a minute. 24/7 = 3.428 minutes, which is equivalent to 3 minutes and 26 seconds, rounding up to the nearest second.

Kerry says
April 14, 2019 @ 01:32

Yeah this is a combined rate/work algebra problem and definitely does have a correct mathematical answer.

Dan says
June 6, 2019 @ 20:42

As has been mentioned above the correct answer is about 3.429 minutes.
I would just like to add that one could treat this problem as the equivalent resistance of two parallel resistors in an electric circuit.