Answer to Question #166293 in Math for Aaron Adem

Question

The number of men needed to cement a barangay road vanes directly with the length of the road at a constant

width and inversely with the number of days required to do the job. If a 30m road can be cemented by 10 men in

12 days how wide is the road? How many days will it take 50 men to cement a road that is 1 km long?

Answer 1

Let $N=$ the number of men needed, $L=$ the length of the road, and

$t=$ the number of days required to do the job. Then

$$N=k\cdot \dfrac{L}{t}$$

Given $N_1=10, L_1=30\ m, t_1=12\ days,$

$N_2=50, L_2=1\ km=1000\ m$

Find $t_2$

$$\dfrac{N_2}{N_1}=\dfrac{k\cdot \dfrac{L_2}{t_2}}{k\cdot \dfrac{L_1}{t_1}}$$

$$N_2\cdot\dfrac{L_1}{t_1}=N_1\cdot\dfrac{L_2}{t_2}$$

$$t_2=t_1\cdot\dfrac{N_1\cdot L_2}{N_2\cdot L_1}$$

$$t_2=12\cdot\dfrac{10\cdot 1000}{50\cdot 30}=80(days)$$

A 1 km road can be cemented by 50 men in 80 days.