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7 October, 05:30

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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  1. 7 October, 09:00
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    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
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