The cost of serving a car is partly varies with the time it takes to do work it costs 2500 for 2hrs service and 4000 for 3whole number 1/2hrs service find :@ the formulae connecting cost c and time t
B t when c =7500
To find the formula connecting cost (c) and time (t) for servicing a car, we need to analyze the given information and determine the relationship.
We are given that the cost of service varies with the time it takes to do the work. We are also given two data points: 2500 for 2 hours of service and 4000 for 3 and a half hours of service.
We can start by considering the cost per hour and see if there is a consistent pattern. Let's calculate the cost per hour for the two given data points:
For 2 hours:
Cost = 2500
Cost per hour = 2500 / 2 = 1250
For 3 and a half hours:
Cost = 4000
Cost per hour = 4000 / (3 + 1/2) = 4000 / (3.5) = 1142.86 (approximately)
From these calculations, we can observe that the cost per hour is not constant. However, we can see that the cost per hour decreases as the duration of service increases.
To find the formula connecting cost (c) and time (t), we can assume a linear relationship between the cost and time. We can express this relationship as:
c = mt + b
where:
c = cost
t = time
m = slope of the line
b = y-intercept (the cost when time is zero)
To calculate the slope (m) and y-intercept (b), we can use the data points we have:
Using (2, 2500):
2500 = 2m + b
Using (3.5, 4000):
4000 = 3.5m + b
We now have a system of two linear equations with two variables (m and b). We can solve this system of equations to find the values of m and b.
Subtracting the first equation from the second equation to eliminate b, we get:
4000 - 2500 = 3.5m - 2m
1500 = 1.5m
m = 1500 / 1.5
m = 1000
Substituting the value of m in the first equation:
2500 = 2(1000) + b
2500 = 2000 + b
b = 2500 - 2000
b = 500
So, the formula connecting cost (c) and time (t) is:
c = 1000t + 500
To find the time (t) when the cost (c) is 7500, we can substitute c = 7500 into the equation and solve for t:
7500 = 1000t + 500
7000 = 1000t
t = 7000 / 1000
t = 7
Therefore, when the cost is 7500, the time taken for service would be 7 hours.