The number of minutes after Abe begins for the three of them to finish painting the room is; 344 minutes
We are told that Abe can paint the room in 15 hours.
Converting to minutes gives; 15 × 60 = 900 minutes
If the area of the room to be painted is x.
Then area painted per minute is; x/900
Now Bea paints 50% faster than Abe. Thus, rate bee can paint per minute is; 1.5x/900
Now,coe can paint twice as fast as Abe. Thus, rate coe can paint per minute is; 2x/900
Abbey works alone for the first hour and half. Thus, this is 90 minutes. Area covered by him in 90 minutes = (x/900) × 90 = x/10
- Now, Bea joins Abe, and they work together until half the room is painted. Thus;
x/10 + (x/900)t + (1.5x/900)t = x/2
Multiply through by 900 to get;
90x + xt + 1.5xt = 450x
Divide through by x to get;
90 + t + 1.5t = 450
2.5t = 360
t = 360/2.5
t1 = 144 minutes
- Now, Coe joins Abe and Bea, and they work together until the entire room is painted. Thus;
(x/900)t + (1.5x/900)t + (2x/900)t = x/2
Multiply through by 900/x to get;
t + 1.5t + 2t = 450
4.5t = 450
t = 450/4.5
t2 = 100 minutes
Thus, total time = 144 + 100
Total time = 244 minutes
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