Any tips for solving problems like this?

Question

Can anyone give me any tips for solving problems like this , I can't get my head around it .

Answer 1

We can consider the "labor-hours" it takes to build a shed. We can interpret a "labor-hour" as the amount of work (progress towards completing a shed) that a single person completes in one hour.

However, Belinda and her neighbor are not equally efficient. Let $B$ denote how much progress Belinda makes towards completing a shed in one hour and let $N$ denote how much progress her neighbor makes towards completing the shed in one hour.

Now we can set up some equations. We see that Belinda and her neighbor working together take $22$ hours to build a shed. So we come up with the equation:

$$22(B+N) = S$$

Where $S$ is the amount of work needed to build a shed. Our second equation is

$$38N = S$$

Since her neighbor takes $38$ hours to build the shed. Then we see that:

$$N = \frac{S}{38}$$

Plugging this back in to our first equation, we find:

$$22(B+\frac{S}{38})=S$$

$$22B=\frac{8}{19}S$$

$$B=\frac{4}{209}S$$

So if Belinda works for one hour, she makes $\frac{4}{209}$ progress towards building a complete shed. Then we see that $\frac{209}{4}$ hours of Belinda working alone builds the complete shed.

Answer 2

HINT: The standard approach is to transform everything into work rates, i.e., the fraction of the job done in one time unit. Here the natural time unit is the hour, and we’re told that the neighbor does $\frac1{38}$ of the job in an hour, while the two together do $\frac1{22}$ of the job in an hour. From this you can work out what fraction of the job Belinda can do in an hour, and from that you easily get the number of hours that she’ll require to do it on her own.