Stan and Hilda can mow the lawn in 20 minutes if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone?
1 hour
stan speed = s lawns/min
Hilda speed = 2s lawns/min
(s + 2s) = total speed in lawns/min
so
(s + 2s) (20 min) = 1 lawn
60 s = 1
s = 1/60 lawns/min
or
60 min/lawn
Yes, an hour, 60 min
Well, let's calculate this. If we assume that Stan's speed is 'x,' then Hilda's speed would be '2x.'
When they work together, their combined speed is x + 2x = 3x.
Now, we know that they can mow the lawn in 20 minutes if they work together, so we can set up the equation: 1/3x = 20.
If we solve this equation for x, we get x = 60.
So, Stan's speed is 60, which means it would take him 60 minutes to mow the lawn alone.
But hey, if he's anything like me, he'll probably take frequent breaks to do an imaginary stand-up routine for the grass! 🌱🤡
To answer this question, we need to understand the concept of work rate. Work rate is a measure of how much work an individual or a group can complete in a given amount of time.
Let's denote Stan's work rate as S (in units of lawn area per minute) and Hilda's work rate as H. Since Hilda works twice as fast as Stan, we can say that H = 2S.
When Stan and Hilda work together, their work rates are combined. So the combined work rate of both is S + H.
We are given that when they work together, they can complete the entire lawn in 20 minutes. This means that their combined work rate is equal to 1/20 (since they complete one full lawn in 20 minutes).
So, we have the equation S + H = 1/20.
Substituting H = 2S, we can rewrite the equation as S + 2S = 1/20.
Combining like terms, we get 3S = 1/20.
Dividing both sides by 3, we find that S = 1/60.
Therefore, Stan's work rate is 1/60 of the lawn area per minute.
To find out how long it would take Stan to mow the lawn alone, we need to calculate the time it would take for Stan to complete one lawn. Let's denote this time as T.
Since Stan's work rate is 1/60 of the lawn area per minute, we can say that Stan can complete 1 T worth of work in 1 minute.
Therefore, T = 1/60.
Hence, it would take Stan 1/60 minutes to mow the lawn alone, which is equivalent to 1 minute.