Question

The number of phone calls between two​ cities, N, during a given time period varies directly as the populations p 1 and p 2 of the two cities and inversely as the​ distance, d, between them. If 18 comma 000 calls are made between two cities 310 miles apart and the populations of the cities are 15 comma 500 and 180 comma 000​, how many calls are made between two cities with populations of 100 comma 000 and 160 comma 000 that are 435 miles​ apart?

Answer 1

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.

Explanation:

Given that,

The number of phone calls between two cities (N )

• directly proportional as the value of populations
  `p_1` and
  `p_2` of two cities.
• Inversely varies as the magnitude of distance (d).

`N\propto(p_1p_2)/(d)`

`N=k.(p_1p_2)/(d)`

Given that,

N=18,000, d=310 miles,
`p_1`=15,500 and
`p_2`=180,000

`18,000=k.(15,500* 180,000)/(310)`

`\Rightarrow k=(18,000*310)/(15,500* 180,000)`

`\Rightarrow k=(31)/(15,500)`

Now,

N=? , d=435 miles,
`p_1`=100,500 and
`p_2`=160,000

`N=(31)/(15,500).(100,000* 160,000)/(435)`

`\Rightarrow N\approx 73,563`

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.