Perry, maria, and lorna are painting rooms in a college dormitory. working alone, perry can paint a standard room in 3 hours, maria can paint a standard room in 2 hours, and lorna can paint a standard room in 2 hours 30 minutes. perry, maria, and lorna have decided that, to speed up the work, 2 of them will paint a standard room together. select the value closest to the shortest time in which a 2-person team could paint a standard room, and select the value closest to the longest time in which a 2-person team could paint a standard room, with each person working at his or her respective rate. make only two selections, one in each column.

Perry and Lorna take the maximum time and Maria and Lorna take the minimum time when they work together.

Explanation: Since, according to the question- Perry takes time when he works alone = 3 hours

Similarly, Maria takes = 2 hours, While Lorna takes= 2 hours 30 minutes or 2.5 hours.

since, there are three people thus their are three possibility to choose any two of them.

1- when Perry and Maria work together then time taken by them is == 6/5= 1 hour 12 minutes.

2- when Maria and Lorna work together then time taken by them is = 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min

3- when Perry and Lorna work together then time taken= = 15/11= 1 hour 4/11 minutes≈ 1 hours 21 minutes

From the above explanation, it has been proved that when we talk about 2 members team then Perry and Lorna take the maximum time. While Maria and Lorna take the minimum time when they work together.

We know that
1) perry can paint a standard room in 3 hours
so
100% of the room> 3 hours
x%> 1 hour
x=100/3< x=33.33%

2) maria can paint a standard room in 2 hours
so
100% of the room> 2 hours
x%> 1 hour
x=100/2< x=50%

3) lorna can paint a standard room in 2.5 hours
so
100% of the room> 2.5 hours
x%> 1 hour
x=100/2.5< x=40 %

therefore
perry can paint 33.33% of a standard room in 1 hour
maria can paint 50 % of a standard room in 1 hour
lorna can paint 40 % of a standard room in 1 hour

Part a) Find the value closest to the shortest time in which a 2-person team could paint a standard room
the value closest to the shortest time is which maria and lorna

team (maria +lorna) =(50%+40%)> 90%  in 1 hour
so
90%> 1 hour
100%> x
x+100/90> x=1.11 hours> 1 h 7 min

Part b) Find the value closest to the longest time in which a 2-person team could paint a standard room
the value closest to the longest time is which perry and lorna

team (perry+lorna) =(33.33%+40%)> 73.33%  in 1 hour
so
73.33%> 1 hour
100%> x
x+100/73.33> x=1.36 hours> 1 h 22 min

it is because 20 + 20 is 40 and then 40 - 20 = 20