Form And Solve Linear And Quadratic Equations

Form And Solve Linear And Quadratic Equations | Extended Abstract Task

Painting Triplets

"Pania, Henare and Matiu are triplets. Henare can paint a room in 3 hours, Pania can do it in 4 hours, Matiu can do it himself in 6 hours, If they all do it work together but don't get in each other's way, how long will it take to paint the room?"

1hr and 20 mins. The reason why is all of them paints a fraction of the room. p + h + m = 1. Since Matiu can do it in 6 hours, that means Henare can do it in half the time. That means that m/2 = h as it means Henare can do a whole room in half the time Matiu takes. So if Pania takes 4 hours, that means she will always be painting 3/4 of the room, because Henare takes 3 hours to paint the whole room. Henare paints h of the room, Pania paints 3h/4. So Pania is 3h/4. 3h/4 = P. Our whole equation is h + 3h/4 + h/2 = 1 or 9/4h = 1 or h. Which I'm pretty sure equals 4/9. Henare takes 3 hours to do the room on his own. This means that he takes 4/9 of 3 hours with his siblings. Painting the room takes 4/3 of an hour or 1 hr and 20 minutes.

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