The number of long distance phone calls between two cities in a certain time period varies jointly as the populations of the cities, p 1 and p 2p1 and p2 , and inversely as the distance between them. If 90 comma 00090,000 calls are made between two cities 600600 miles apart, with populations of 120 comma 000120,000 and 110 comma 000110,000 , how many calls are made between cities with populations of 100 comma 000100,000 and 90 comma 00090,000 that are 400400 miles apart?

Question

Mathematics

Cade Terrell

9 August, 03:28

The number of long distance phone calls between two cities in a certain time period varies jointly as the populations of the cities, p 1 and p 2p1 and p2 , and inversely as the distance between them. If 90 comma 00090,000 calls are made between two cities 600600 miles apart, with populations of 120 comma 000120,000 and 110 comma 000110,000 , how many calls are made between cities with populations of 100 comma 000100,000 and 90 comma 00090,000 that are 400400 miles apart?

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Brendan Cordova · Answer 1

90,000 calls

Step-by-step explanation:

Number of calls between cities is directly proportional to their populations & inversely related to the distance between them.

Let no. of calls be = c; populations = p1 & p2; distance = d, proportion constant = k

So, c = (k p1 p2) / d

Given: c = 90000, p1 = 120000, p2 = 110000, d = 600

90000 = [ k (120000) (110000) ] / 600

90000 = k 22,000,000

k = 90000 / 22,000,000 = 0.004

To find : - c at (p1, p2) = 100000, 90000 & d = 400

c = [ 0.004 (100000) (90000) ] / 400

= 36000000 / 400

= 90,000 calls