Question

One member of a gardening team can landscape a new lawn in 36 hours. The other member of the team can do the job in 45 hours. How long would it take to landscape a lawn if both gardeners worked together?

Answer 1

20 hours

Explanation:

rate and time are inverses of each other.

If it takes one 36 hours, so his rate is:

1/36

It takes another 45 hours, so his rate is:

1/45

Since they will work together, their combined rate will be:

1/36 + 1/45

Now, we want the TIME IT WILL TAKE THEM, so we inverse their combined rate, that is we take the combined rate and raise it to -1st power. The calculation is shown below:

`((1)/(36)+(1)/(45))^(-1)\\=((45+36)/(45*36))^(-1)\\=((81)/(1620))^(-1)\\=(1620)/(81)\\=20`

Thus, if both work together, it will take them 20 hours