Question

John is driving around town. When he reaches the gas station, he notes that he has traveled 20 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.

If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?

Answer 1

d = 5t + 20

Explanation:

d represents the distance and t represents the time, in hours

Let he equation which model this situation ⇒ d = a t + b

Where a and b are constant.

Let the gas station is the starting point

So, at gas station t = 0 , d = 20

∴ 20 = 0 * a + b ⇒ b = 20

When he reaches home 2 hours later notes that he has traveled 30 miles.

and with substituting with b = 20

∴ 30 = 2 * a + 20

2a = 30 - 20 = 10 ⇒ a = 10/2 = 5

∴ d = 5t + 20

The equations that can be used to model this situation d = 5t + 20