Brayden and his friends are driving across the US from New York to Los Angeles at a constant speed without stopping. When they have driven for 10 hours, they are 1700 miles away from Los Angeles. When they have driven for 15 hours, they are 1500 miles away from Los Angeles. a) Find a linear function that models the remaining distance, DD, to Los Angeles as a function of the amount of time, t, that Brayden and his friends have been driving.

d=-40t+2100

Step-by-step explanation:

Let d be the distance between New York to Los Angeles and speed of driving is v miles/hour.

As when they have driven for 10 hours, they are 1700 miles away from Los Angeles, so the distance covered in 10 hours is d-1700 miles.

Similarly, the distance covered in 15 hours is d-1500 miles.

So, the distance covered in 5 hours = (d-1500)-(d-1700) =d-1500-d+1700=200 miles.

As speed = distance/time,

So the speed of driving, v=200/5=40 miles/hour

Let d (in miles) be the remaining distance at any time instant t (in hour) and the linear relation between d and t is

d=at+b ...(i)

where a and b are constants.

When they have driven for 10 hours, they are 1700 miles away from Los Angeles, so putting t=10 and d=1700 in the equation (i), we have

1700=10a+b

b=1700-10a...(ii)

Similarly, when they have driven for 15 hours, they are 1500 miles away from Los Angeles, so

1500=15a+b

1500=15a+1700-10a

1500-1700=5a

-200=5a

a= -200/5

a= -40

From equation (ii), we have

b=1700-10(-40)=1700+400=2100

From equation (i), the required equation is

d=-40t+2100

Hence the required linear function is d=-40t+2100.