Please help me with the following problem:
Joe is on a cross-country trip from New York to Los Angeles. He drives for 45.0 min at 70.0 km/h, 10.0 min at 95 km/h, and 30.0 min at 55.0 km/h, and he spends 20.0 min eating lunch and buying gas. What is the average speed for this part of his trip?
a. 67.6 km/h
b. 68.4 km/h - I did b as a guess, because I couldn't figure the answer, but I got it wrong
c. 54.7 km/h
d. 53.8 km/h
I have no idea on how to do this. I have tried distance over time tons of times, and I get different answers than the ones above. Can you guys help me please? I will greatly appreciate it.
One of the things that I did was:
Delta d
--------
Delta t
and I did:
m - m
-------
s - s
distance is m
time is s
I did both of them, but I get different answers. Thanks, if you guys help. :)
its 54.7 km/s
To find the average speed, you need to calculate the total distance traveled and the total time taken. Let's break down the problem step by step:
1. Start by calculating the distance traveled at each speed:
- For the first part of the trip (45.0 min at 70.0 km/h), the distance covered is:
distance = speed * time = 70.0 km/h * 45.0 min / 60 min/h
- For the second part of the trip (10.0 min at 95 km/h), the distance covered is:
distance = speed * time = 95 km/h * 10.0 min / 60 min/h
- For the third part of the trip (30.0 min at 55.0 km/h), the distance covered is:
distance = speed * time = 55.0 km/h * 30.0 min / 60 min/h
2. Next, calculate the total distance traveled by summing up the distances from each part of the trip.
3. Calculate the total time taken by summing up the time for each part of the trip, including the time for eating lunch and buying gas.
4. Finally, divide the total distance by the total time to find the average speed.
Let's go through each step to find the solution:
1. First part of the trip:
distance = 70.0 km/h * 45.0 min / 60 min/h = 52.5 km
2. Second part of the trip:
distance = 95 km/h * 10.0 min / 60 min/h = 15.8 km
3. Third part of the trip:
distance = 55.0 km/h * 30.0 min / 60 min/h = 27.5 km
4. Total distance traveled:
total distance = 52.5 km + 15.8 km + 27.5 km = 95.8 km
5. Total time taken:
total time = 45.0 min + 10.0 min + 30.0 min + 20.0 min = 105.0 min
6. Average speed:
average speed = total distance / total time = 95.8 km / 105.0 min * 60 min/h = 54.86 km/h (rounded to two decimal places)
Therefore, the average speed for this part of Joe's trip is approximately 54.9 km/h.
Based on the answer choices you provided, the closest option is:
c. 54.7 km/h
It seems there might be a slight rounding error in the answer choices. The correct answer should be the closest match, so c. 54.7 km/h would be the best option.