A car enters a turnpike 22 miles north of a town. The car travels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours?
How do you solve the linear function then solve the problem?
If you could help me understand this it would be amazing because I have a test soon and I actually want to know how to do it.
y = m x + b
here
distance = 4 (speed) + 22
Distance is a function of time. The constant rate of change is 64. Write the equation y = 64x + 22. Substitute 4 in for x to get 278 miles.
22 + distance traveled after entering pike
= 22 + 4 * 64
= 22 + 256
= 278 miles
This is just like the taxi problem really.
You are already 22 miles north
then
you travel 4 * 64 miles
To solve this problem using a linear function, we need to understand that the car's distance from the town is increasing at a constant rate of 64 miles per hour in the north direction.
Let's start by setting up a linear function:
Distance = Rate × Time
In this case, the rate the car is traveling at is 64 miles per hour, and we want to find the distance after 4 hours. So, using the formula, we have:
Distance = 64 miles/hour × 4 hours
To find the distance, we simply multiply the rate by the time:
Distance = 256 miles
Therefore, after 4 hours, the car will be 256 miles north of the town.
To solve this problem, it's important to understand the concept of rate (speed) and the relationship between rate, time, and distance in a linear function. Make sure to read the problem carefully and identify the given information and what you want to find. Then, set up the equation using the formula Distance = Rate × Time, and plug in the values to calculate the answer.
Practicing similar problems and understanding the underlying concept will help you solve linear function problems more effectively. Good luck with your test!