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# Three different lumberjacks can chop W amount of wood in 30 minutes, 4

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Re: Three different lumberjacks can chop W amount of wood in 30 minutes, 4 [#permalink]
Lumberjack who complete 1 unit of work (1W) in complete in 30 mins => In 1 hour he will complete 2 unit of work (2W)

Lumberjack who complete 1 unit of work (1W) in complete in 45 mins (45/60 = 3/4 hr) => In 1 hr he will complete 4W/3 = 1.33 units of work

Lumberjack who complete 1 unit of work (1W) in complete in 50 mins (50/60 = 5/6 hr) => In 1 hr he will complete 6W/5 = 1.2 units of work

Two fastest lumberjacks -> who complete more amount of work in a hr -> Lumberjacks who completed work in 30 mins and 45 mins resp.

Together in 1 hr, 2 fastest lumberjacks will complete --> 2W + (4W/3) = 10W/3 work

Hence, in 2 hrs, they will do 2 * (10W/3) = 20W/3 --> 6.66 Work ---> Option A.
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Re: Three different lumberjacks can chop W amount of wood in 30 minutes, 4 [#permalink]
Bunuel wrote:
Three different lumberjacks can chop W amount of wood in 30 minutes, 45 minutes, and 50 minutes according to their different levels of skill with the axe. How much wood, in terms of W, could the two fastest lumberjacks chop in 2 hours?

A. $$6 \frac{2}{3} W$$

B. 6 W

C. $$4 \frac{2}{3} W$$

D. 3 W

E. $$2 \frac{2}{3} W$$

A = time taken to chop 1 wood by A
B = time taken to chop 1 wood by B

Since (1/A)*(30/60) = W
Therefore 1/A = 2W

(1/B)*(45/60) = W
Therefore 1/B = 4W/3

(1/A+1/B)*2 = x (amount of wood to be chopped in 2 hours)
= [2W + 4W/3]*2 = 20W/3
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Re: Three different lumberjacks can chop W amount of wood in 30 minutes, 4 [#permalink]
Bunuel wrote:
Three different lumberjacks can chop W amount of wood in 30 minutes, 45 minutes, and 50 minutes according to their different levels of skill with the axe. How much wood, in terms of W, could the two fastest lumberjacks chop in 2 hours?

A. $$6 \frac{2}{3} W$$

B. 6 W

C. $$4 \frac{2}{3} W$$

D. 3 W

E. $$2 \frac{2}{3} W$$

Let's say the W amount of work done = 1, and we know that the two fastest lumberjacks (say x and y) can chop the wood in 30minutes ( = 1/2 hr) and 45 minutes (= 3/4 hr).

work rate * time = amount of work ===> (W/x + W/y) * 2 = (1/x + 1/y) * 2 = [1/(1/2) + 1/(3/4)] * 2 = (2/1 + 4/3) * 2 = 10/3 * 2 = 20/3 = 6 2/3

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Re: Three different lumberjacks can chop W amount of wood in 30 minutes, 4 [#permalink]
Bunuel wrote:
Three different lumberjacks can chop W amount of wood in 30 minutes, 45 minutes, and 50 minutes according to their different levels of skill with the axe. How much wood, in terms of W, could the two fastest lumberjacks chop in 2 hours?

A. $$6 \frac{2}{3} W$$

B. 6 W

C. $$4 \frac{2}{3} W$$

D. 3 W

E. $$2 \frac{2}{3} W$$

2 fastest lumberjacks are 30 min one and 45 minute one. In 2 hours, 30 minute one can chop 4, while 45 minute one can do >2. Only A is greater than 6. Answer is A
Re: Three different lumberjacks can chop W amount of wood in 30 minutes, 4 [#permalink]
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