Question

It takes 54 minutes for 4 people to paint 6 walls. How many minuets does it take 6 people to paint 7 walls?

Answer 1

It takes 42 minutes for 6 people to paint 7 walls

Solution:

It takes 54 minutes for 4 people to paint 6 walls

To find: Minutes required for 6 people to paint 7 walls

If $M_1$ men can do $W_1$ work in $D_1$ days working $H_1$ hours per day and $M_2$ men can do $W_2$ work in $D_2$ days working $H_2$ hours per day, then

$\frac{M_1D_1H_1}{W_1} = \frac{M_2D_2H_2}{W_2}$

M = Number of men

D = Number of days

H = Number of hours per day

W = Amount of work

Here in this sum,

54 minutes for 4 people to paint 6 walls

$H_1 = 54 minutes ; M_1 = 4 people ; W_1 = 6 walls$

Minutes required for 6 people to paint 7 walls

$H_2 = ? ; M_2 = 6 people ; W_2 = 7 walls$

Substituting the values in formula, we get

$\frac{54 \times 4}{6} = \frac{H_2 \times 6}{7}\\\\9 \times 4 = \frac{H_2 \times 6}{7}\\\\H_2 = \frac{36 \times 7}{6}\\\\H_2 = 42$

Thus it takes 42 minutes for 6 people to paint 7 walls