Question

a large snow plow can clear the west main parking lot in 4 hours. A small snowplow needs more time to clear that lot. working together, they can clear the lot in 3 hours. how long would it take the small plow to clear the lot by itself?

Answer 1

Answer: 12 hours

Step-by-step explanation:

s = the time of the smaller plow.

In one hour, the larger can do 1/4 of a lot, right?  Then, the smaller plow can do 1/s of a lot.

Working together to do 1 lot, we multiply their rates by the time.

1/4(3) + 1/s(3) = 1

3/4 + 3/s = 1

The common denominator is 4s, so...

3s/4s + 12/4s = 1

With a common denominator, we can now combine the numerators...

(3s+12)/4s = 1

We multiply both sides by 4s...

3s + 12 = 4s

       12 = s

So, it would take the smaller plow 12 hours to clear the lot by itself.