The time, t hours, required to complete a road maintenance project varies inversely as the… — JAMB UTME

The time, $t$ hours, required to complete a road maintenance project varies inversely as the number of workers, $w$ , assigned to the project. If 8 workers can finish the project in 15 hours, calculate the time, in hours, required for 12 workers to finish the same project.

Answer: 10 hours

Answer

10 hours

Because the time

t

varies inversely as the number of workers

w

, the total worker-hours required for the project is constant:

k = 8 \times 15 = 120

worker-hours. Dividing this total work by 12 workers gives

\frac{120}{12} = 10

hours.

Step-by-Step Solution

Set up the inverse variation equation

t = \frac{k}{w}

, where

k

is the constant of variation.

Inverse variation implies that as the number of workers increases, the time required decreases proportionally.

Determine the value of the constant of variation

k

k = t \times w = 15 \times 8 = 120

Substitute the known pair of values (

w = 8, t = 15

) into the equation.

Compute the new value of

t

for 12 workers

t = \frac{120}{12} = 10

hours.

Substitute

w = 12

and

k = 120

into

t = \frac{k}{w}

Key Concept

Inverse Variation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic