Question

16) Imani can pick forty bushels of apples in 8.2hours. Chelsea can pick the same amount in10.8 hours. How long would it take them ifthey worked together?

Answer 1

Imani picked up 40 bushels of apple in 8.2 hours.

And Chelsea picked up 40 bushels of apple in 10.8 hours

Let I be Imani ratio, hence we have

`I=(40)/(8.2)`

and let C be Chelsea ratio, hence,

`C=(40)/(10.8)`

Now, let T be the ratio when Chelsea and Imani work together. In this case, we have

`T=(40)/(t)`

where t is the time for their work.

This means that,

`I+C=T`

that is, this equality must be fulfilled in order to compare both cases. Hence,

`(40)/(8.2)+(40)/(10.8)=(40)/(t)`

we can factorize 40 in both sides, hence, we have that

`(1)/(8.2)+(1)/(10.8)=(1)/(t)`

Now, we must solve this equality for t. Therefore, we have

`(10.8+8.2)/((10.8)(8.2))=(1)/(t)`

or

`(19)/(88.56)=(1)/(t)`

it yields,

`0.2145=(1)/(t)`

Finally, t is equal to

`\begin{gathered} t=(1)/(0.2145) \\ t=4.66 \end{gathered}`

that is, of they work together, they will take 4.66 hours only