You are driving home on a weekend from school at 65mph for 130 miles. It then starts to snow and you slow to 45 mph. You arrive home after driving 4 hours. How far is your hometown from school?

First I found the time with d/v=t so 130/65= 2 hours

I used d= d_0 +vt
=130 +45(6)
=400 miles

I plugged in 6 hours for the time from adding 2 hours and 4 hours.
Is this correct?

You covered 130 miles in the first two hours (130/65 = 2). You then traveled 45 mph for 2 hours, so you went 90 miles (45*2).

130 + 90 = 220 miles

No, your calculation is not correct. Let's go through the problem step by step.

First, let's find the time it took for you to drive at 65 mph. As you correctly calculated, the distance traveled at this speed is 130 miles, so we can use the formula d = vt and solve for t:

t = d / v
t = 130 miles / 65 mph
t = 2 hours

So, it took you 2 hours to cover the initial 130 miles.

Next, you slowed down to 45 mph for the remaining distance. We know that the total time for the entire trip was 4 hours, and you already traveled for 2 hours, so the time spent driving at 45 mph can be calculated as:

time at 45 mph = total time - time at 65 mph
time at 45 mph = 4 hours - 2 hours
time at 45 mph = 2 hours

Now, we can use the formula d = vt to find the distance traveled at 45 mph:

d = v * t
d = 45 mph * 2 hours
d = 90 miles

So, the remaining distance from your hometown is 90 miles.

To get the total distance between your hometown and school, we can add the initial 130 miles to the remaining 90 miles:

Total distance = initial distance + remaining distance
Total distance = 130 miles + 90 miles
Total distance = 220 miles

Therefore, your hometown is 220 miles away from school, not 400 miles as you calculated.