Question

Manav is painting a rectangular room and the dimensions of this room are given by x,y and z feet. Manav takes 8 hours to paint a wall with dimensions x and z. He takes 4 hours to paint a wall with dimensions y and z and 12 hours to paint the ceiling which has dimensions x and y. Manav works at a constant rate. X=6, what is the volume of the room?

A.) 18 cubic feet
B.) 36 cubic feet
C.) 24 cubic feet
D.) 30 cubic feet
E.) 32 cubic feet
F.) 34 cubic feet

Answer 1

Answer:

B) 36 cubic feet

Step-by-step explanation:

Dimensions of the room are x, y and z feet. It is given that x = 6 feet.

Manav took 8 hours to paint the wall with dimensions x and z.

This means, in 8 hours Manav painted area = xz = 6z

In 1 hour Manav painted area = $\frac{6z}{8}$

Manav took 4 hours to paint the wall with dimensions y and z.

This means, in 4 hours Manav painted area = yz

In 1 hour Manav painted area = $\frac{yz}{4}$

Manav took 12 hours to paint the ceiling with dimensions x and y.

This means, in 12 hours Manav painted area = xy = 6y

In 1 hour Manav painted the area = $\frac{6y}{12}=\frac{y}{2}$

Since, Manav works at constant rate, this means the worked done in 1 hour in all 3 cases would be the same. So we can write:

$\frac{6z}{8}=\frac{yz}{4}=\frac{y}{2}$

Using the first two equations, we get:

$\frac{6z}{8}=\frac{yz}{4}\\\\ \frac{6}{8}=\frac{y}{4}\\\\ y=\frac{6}{8} \times 4\\\\ y = 3$

Using the last two equations, we get:

$\frac{yz}{4}=\frac{y}{2}\\\\ \frac{z}{4}=\frac{1}{2}\\\\z=2$

So, we have the follwoing dimensions of the room:

x = 6 feet

y = 3 feet

z = 2 feet

So the volume of the room is =  6 x 3 x 2 = 36 cubic feet