Question

D varies as R and S, and inversely as t. D=12, R=3, S=20, and t=5, find D when R=15, S=4 and t=8.

Answer 1

Given:

D varies as R and S, and inversely as t.

D=12, R=3, S=20, and t=5

To find:

The value of D when R=15, S=4 and t=8.

Solution:

It is given that D varies as R and S, and inversely as t. So,

`D\propto (RS)/(t)`

`D=(kRS)/(t)` ...(i)

Where, k is the constant of proportionality.

We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get

`12=(k(3)(20))/(5)`

`12=12k`

`(12)/(12)=k`

`1=k`

Substituting
`k=1` in (i), we get the required equation.

`D=((1)RS)/(t)`

`D=(RS)/(t)`

We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get

`D=((15)(4))/(8)`

`D=(60)/(8)`

`D=7.5`

Therefore, the required value of D is 7.5.