Question

If t varies as v, and t = 2 4/7 when v =13/14 , find v when t = 2 1/4

a) 2106/392
b) 13/16
c) 324/52

Answer 1

Answer : b) 13/16

Given : t varies as v

So t = k v where k is the constant of proportionality.

t = 2 4/7 when v =13/14. Using these values we find out k

`t = 2(4)/(7) =(18)/(7)`

`v =(13)/(14)`

t = k * v

`(18)/(7)= k *(13)/(14)`

Multiply by 14/13 on both sides

`(18)/(7) *(14)/(13) = k *(13)/(14)*(14)/(13)`

So
`k =(36)/(13)`

We got the value of k. Now we find v when t = 2 1/4

`t = 2(1)/(4) =(9)/(4)`

t = k * v

We know the value of t and k

`(9)/(4)= (36)/(13)* v`

Multiply by 13/36 on both sides

`(9)/(4) *(13)/(36) =(36)/(13)*(13)/(36)* v`

So
`(13)/(16)= v`

Option B is correct