Question

The distance an electric car can travel on one full charge depends on the speed of the car. The table shows the approximate distances a certain model of electric car can travel on one full charge
when moving at various constant speeds.
The speed and the corresponding distance form an arithmetic sequence, where the speed represents the number of the term and the corresponding distance represents the value of the term.
What is the distance, in miles, that the car can travel on one full charge when moving at a constant speed of 75 miles per hour (mph)?
A) 220
B250
С270
D290

Answer 1

Answer:

Distance covered by the car = 220 miles

Step-by-step explanation:

Speed (mph) (s)             Distance (miles) (d)     Difference in distances

      45                               400                                        -

      50                               370                            400 - 370 = 30

      55                               340                            370 - 340 = 30

      60                               310                             340 - 310 = 30

      65                               280                            310 - 280 = 30

Since differences between each successive term of the distances are common,

Therefore, table represents a linear function.

Let the equation representing the relation between the speed and distance is,

d = ms + c

Where m = slope of the line

And c = y-intercept

For a point (45, 400) lying on the line,

400 = 45m + c ----- (1)

Similarly, for a point (60, 310),

310 = 60m + c -------(2)

Equation (1) - equation (2)

400 - 310 = 45m - 60m

90 = -15m

m = -6

By substituting m = -6 in equation (1),

400 = 45(-6) + c

c = 400 + 270

c = 670

Therefore, equation will be,

s = -6d + 670

Now we have to calculate the distance covered by the car when moving with a constant speed of 75 mph,

d = -6(75) + 670

d = 670 - 450

d = 220 miles