Problema Solution
The number of long distance calls between two
cities in a certain time period varies jointly
as the population of the cities P1 and P2, and
inversely as the distance between them. If 70,000
calls made between two cities 400 miles apart
with populations of 120,000 and 100,000, how many
calls are made between cities with populations
70,000 and 60,000 that are 300 miles apart?
Answer provided by our tutors
let
n = the number of long distance calls
d = the distance between the cities
p1, p2 the population of the cities P1 and P2
n = k(p1 * p2)/d, where k is constant
First we will find k
70,000 calls made between two cities 400 miles apart with populations of 120,000 and 100,000 that is
n = 70000, d = 400 miles, p1 = 120000, p2 = 100000
7000 = k(120000*100000)/400
by solving the equation for k we find
k = 7000*400/(12* 10^4 * 10^5)
k = 28*10^5/(12*10^9)
k = (28/12)*10^(-4)
k = (7/3) *10^(-4)
how many calls are made between cities with populations 70,000 and 60,000 that are 300 miles apart?
p1 = 70000 = 7*10^4
p2 = 60000 = 6*10^4
d = 300
n = ?
n = k(p1 * p2)/d
n = (7/3) *10^(-4)*(7 * 10^4 * 6 * 10^4)/300
n = (7/3)*7*6*10^4/300
n = 3266.67 calls
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there are 3267 calls made.