Question

9. Carlos is taking a road trip. So far he has traveled 120 miles at a constant speed of 60 mph. His

distance can be modeled by the function d(x) = 60x + 120, where x is in hours. How many miles
will he have traveled after 3,5, and 8 more hours? Interpret the results in terms of the context of
the function.

Answer 1

Part 1) 300 miles

Part 2) 420 miles

Part 3) 600 miles

Explanation:

we have

`d(x)=60x+120`

where

d(x) is the distance in miles

x is the time in hours

Part 1) How many miles will he have traveled after 3 more hours?

we know that

To find the distance, substitute the value of x in the function

so

For x=3 hours

`d(3)=60(3)+120=300\ mi`

For x=3, d(x)=300

That means -----> After 3 hours Carlos has traveled 300 miles at a constant speed of 60 mph

Part 2) How many miles will he have traveled after 5 more hours?

we know that

To find the distance, substitute the value of x in the function

so

For x=5 hours

`d(5)=60(5)+120=420\ mi`

For x=5, d(x)=420

That means -----> After 5 hours Carlos has traveled 420 miles at a constant speed of 60 mph

Part 3) How many miles will he have traveled after 8 more hours?

we know that

To find the distance, substitute the value of x in the function

so

For x=8 hours

`d(8)=60(8)+120=600\ mi`

For x=8, d(x)=600

That means -----> After 8 hours Carlos has traveled 600 miles at a constant speed of 60 mph