Question

1. Total distance traveled varies directly with the amount of time spent traveling. If traveling 4.5 hours results in 180 miles traveled, write the direct linear variation equation. Then determine how long it would take you to travel 320 miles, assuming you traveled at the same rate.

a.What are the variables (the input and output)?
b.Solve for k.
c.Write the direct variation equation.
d. How long will it take you to travel 320 miles?

Answer 1

a) d=kt the input is t and the output is d

b) 180=4.5k k =40

c) d= 40t

d) 320=40t t=8 hours

Answer 2

a) The variables are time and distance, where the input is time and output is distance.
b and c) d is directly proportional to t
d = kt
180 = k(4.5)
k = 40
d) 320 = 40t
t = 8 hours