Emma and Ed walk into a room containing 30 assembled Tworks and enough pieces to assemble 100 more Tworks. A Twork takes eight minutes to assemble and 10 minutes to disassemble. If Emma starts assembling Tworks as Ed begins disassembling the ones that were already made, and they both continue to work until there are exactly 35 assembled Tworks in the room (and no partially assembled or disassembled Tworks), how many minutes will Emma have worked?

Start with 30 assembled, parts for 100 more.

Each minute results in +1/8 and -1/10

So we want

30 + x/8 - x/10 = 35

x/8 - x/10 = 5

5x - 4x = 200

x = 200 minutes

During 200 minutes, 25 are assembled, 20 are disassembled,

resulting in a net gain of 5, added to the original 30.

Bike ride:

Total distance: 40 km

Desired average speed 20 km/hr

Total time will be 2 hours

20 km at 15 km / hr = 4/3 hour taken

Leaves 2/3 hour for 20 km

20 km in 2/3 hour = 30 km/hr

Gas mileage:

Let m = city mileage

m + 3 = highway mileage

136 / (m+3) + 155 / m = 9

9m^2 - 264m - 465 = 0

m = 31 (discarding negative value)

Bricklaying:

Let b = number of bricks in wall

Lisa lays b/9 bricks per hour

Lauren lays b/10 bricks per hour

b = 5 * (b/9 + b/10 - 10)

b = 5b/9 + 5b/10 - 50

90b = 50b + 45b - 4500

b = 900

Lisa does 100 per hour

Lauren does 90 per hour

Together they do 180 per hour.

That's enough work for one Yahoo Question

The tugboat problem, in various forms I have answered before -

it has appeared many times on Yahoo Answers, sometimes with ferry boats,

sometimes with sailboats.

The ant path problem also can be found on the web in many places I am sure.

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gassaway's avatar

gassaway

Lv 4

4 years ago

three. 80x four. 80x + a million five. 250(80x + a million) 6. 250(80x + a million) + y 7. 250(80x + a million) + 2y eight. 250(80x + a million) + 2y - 250 nine. [250(80x + a million) + 2y - 250] / two = [20000x + 250 + 2y - 250] / two = [20000x + 2y] / two = 10000x + y

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Step-by-step explanation:

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.