Respuesta :
Answer:
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.
