can you help i dnt know what to do so could you tell me how to solve it

1. every weekend, Phil drives from his home to his favorite amusement park, a distance of 60 miles.

a. If he averages 40 mph for the first half of the trip, what must his average speed for the second half of the trip in order for him to average 50 mph for the entire trip?

b. Suppose that on the trip home, Phil decides to stop a 30 minute dinner break. If he averages 45 mph for the first half of this return trip and 60 mph for the second half of this trip, how many more MINUTES will the return trip take compared to the trip going to the park? (be sure to account for his dinner break.)

1.a To average Vav = 50 mph for the entire trip, the 60 miles distance (D) must be covered in a total time of

D/Vav = 6/5 = 1.2 hours
The first 30 miles required 30/40 = 0.75 hours. The remaining 30 miles must be completed in 1.2 -0.75 = 0.45 hours.
The average speed for the second half of the trip must be 30/0.45 = 66.7 mph

1.b The trip home is also 60 miles in length. Total travel time with dinner break = 30/45 + 30/60 hrs + 0.5 h = 1.667 h

Remember that it took him 1.2 hours to get TO the park. With the dinner break and return speeds indicated, it takes 0.467 hours longer to get home.

6 years

Sure, I can help you!

For question 1a:

To find the average speed for the second half of the trip, we first need to determine the remaining distance Phil has to travel. Since the total distance is 60 miles and he has already covered the first half of the trip, the remaining distance is also 60 miles.

Now, let's use the formula for average speed:

Average speed = Total distance / Total time

We know that the average speed for the entire trip is 50 mph. Let's denote the average speed for the second half as x mph. We can set up the equation:

50 = (60 + 60) / (t + t)

Simplifying this equation gives us:

50 = 120 / 2t

Now we solve for t (time):

50 * 2t = 120

100t = 120

t = 120 / 100 = 1.2 hours

Now, to find the average speed for the second half, we use the average speed formula again:

x = 60 miles / 1.2 hours

x = 50 mph

Therefore, in order for Phil to average 50 mph for the entire trip, he needs to maintain an average speed of 50 mph for the second half of the trip as well.

For question 1b:

First, let's calculate the time taken for the first half of the return trip. Given that Phil averages 45 mph for the first half, we can calculate the time taken:

Time = Distance / Speed

Time = 60 miles / 45 mph

Time = 4/3 hours or 1 hour 20 minutes

Now let's consider the second half of the return trip. Phil averages 60 mph for this portion. Using the same formula, we calculate the time taken:

Time = Distance / Speed

Time = 60 miles / 60 mph

Time = 1 hour

Now, let's account for Phil's dinner break of 30 minutes. We add this to the total time taken:

Total time = 1 hour 20 minutes + 1 hour + 30 minutes

Total time = 2 hours 50 minutes

So the return trip will take 2 hours and 50 minutes compared to the trip going to the park.

I hope this helps! Let me know if you have any further questions.