Question

Problem Page Bob is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Bob has 62 miles to his destination after 16 minutes of driving, and he has 52.4 miles to his destination after 28 minutes of driving. How many miles will he have to his destination after 42 minutes of driving?

Answer 1

41.2 miles

Explanation:

Let the equation of the line that shows the given situation,

y = mx + c

Where, x shows driving time in minutes and y shows the distance to his destination after x minutes,

m and c are any constant

If y = 62 then x = 16, ( given )

62 = 16m + c -----(1)

Also, If y = 52.4 then x = 28 ( given )

52.4 = 28m + c -----(2)

Equation (1) - equation (2),

9.6 = -12m

`\implies m=-(9.6)/(12)=-0.8`

From equation (1),

62 = 16(-0.8) + c = -12.8 + c

⇒ c = 62 + 12.8 = 74.8

Hence, the equation of line that shows the given situation,

y = -0.8x + 74.8,

If x = 42,

y = -0.8(42) + 74.8 = -33.6 + 74.8 = 41.2

Hence, 41.2 miles will he have to his destination after 42 minutes of driving.