Question

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.

Answer 1

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

Answer 2

Answer: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 $\frac{1}{1/2+1/3}$=$\frac{1}{5/6}$= 6/5= 1 hour 12 minutes.

2- when Maria and Lorna work together then time taken by them is $\frac{1}{1/2 + 1/2.5}$= 10/9= 1 hours 1/9 minutes ≈ 1 hours 7 min

3- when Perry and Lorna work together then time taken= $\frac{1}{1/3+1/2.5}$= 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.