Guide 4 (Word Translations) Chapter 5 [3rd Edition]

[ankitp]

Chapter Q14.

The question states : It takes the average dyer 80 minutes to dry one full load of Bob's laudry. Bob has one average dyer and also decides to try one "Super Jumbo-Tron Dyer Matiic" which is faster than the average dryer by a ratio of 5:4" ...


The last line "faster than the average dryer by a ratio of 5:4" to me would mean

If average dryer speed was X
Jumbo-tron dyer would be X ( 1 + 5/4) = X(9/4)

The reason I believe that is becuase "faster than the average dryer by a ratio of 5:4" is the same as saying "faster than the average dryer by 125%" which would mean 1 + 1.25 = 2.25

Does that make sense?

Thanks in advance,

Ankit

[StaceyKoprince]

Ah, I see what you're saying. When given a ratio, though, don't just try to translate the ratio into a percentage. The ratio is giving you the data for BOTH pieces of info, by definition. One quantity is represented by the 5 and the other is represented by the 4.

[saurabhbanerjeeiimk]

Manhattan Rocks, with an expanded range of questions.

While I have understood the actual solution, I'am confused on the explanation of the question, which shares an "incidental" senario.

Kindly explain how does 4/9 refer to the regular dryer, while how do we get 320/3.

Thank you.

[StaceyKoprince]

In the original problem, we're told that Bob can't move laundry from one machine to another part-way through the drying.

The "incidental" scenario addresses what would happen if we changed the problem to allow Bob to move laundry from one machine to another part-way through.

So the 320/3 answer is only valid if we CHANGE the problem to allow Bob to move the laundry around when it's partially dry.

Does that make more sense? Knowing that, do you have a question about how to solve that changed problem? Work your way as far through as you can and then let us know.

[davetzulin]

i just stumbled on this problem too and I could use some clarification on the "incidental" scenario. Not the original answer to the problem.

The way I picture this is:

- both the fast and the slow start drying their own laundry loads. say loads 1 and 2, so 2 loads are being done concurrently.
- when fast dryer is 5/9 done, the slow is exactly 4/9 done. you do a swap which costs no time.
- now they both can finish at the exact same time.

but then for the third load, they both need to take a part of the final load: 1/2 each. then swap at 5/9 (of 1/2) and 4/9 (of 1/2) again.

so shouldn't the problem say they can actually take a fresh load and split up the work (not just swapping half done loads) for the case of the third load?

and I noticed the time of 107 minutes is actually the same as the sum of their rates (1/80 + 1/64)*T = 1, which makes sense because both are being utilized 100%.

[arnabgangully]

i think the first explaination of 125%+100%=225% is the best one

[tim]

sounds like everyone has a good handle on this one. let us know if there are still any questions..