Question

5. The table shows how far a car is from its destination after x hours.

Hours
Miles
1
150
2
100
50
لیا
3
The function f(x) = 210-60x represents a second trip, where f(x) is the number of miles
the car is from its destination after x hours. Which trip takes less time? Explain.

Answer 1

the trip represented by f(x) takes less time

Explanation:

Given a table of time and distance to go, and a function f(x) = 210-60x representing the same for a different trip, you want to know which trip takes less time.

Table

The table has values ...

(time in hours, remaining distance in miles) = (1, 150), (2, 100), (3, 50)

This shows you the remaining distance decreases by 50 miles for every hour added to the travel time. That means the remaining 50 miles will be reduced to zero after 4 hours.

The trip represented by the table takes 4 hours.

Equation

The function f(x) = 210-60x will have a value of zero when ...

0 = 210 -60x

0 = 3.5 -x . . . . . . divide by 60

x = 3.5 . . . . . . . . add x

The trip represented by the function f(x) takes 3.5 hours.

The second trip takes less time.