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
Two things that I did to help me were:
Delta d
--------
Delta t
and
m - m
-------
s - s
distance is m - m is meters
time is s - seconds
For the second one I did kilometer over hour.
I have no idea on how to do this, and I have no idea of if I am doing it right or not. 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.
average velocity=distance/time
distance=3/4*70+1/6*95 + 1/2*55
time= (45+10+30)/60
check my thinking. I get none of the answers.
Okay, I get what you did, but is there other ways of doing this?
Also, why did you convert the minutes into seconds, but in fraction form?
The home-school lesson did not teach me how to do that. I don't understand why you would turn it into a fraction, can you explain it to me?
3/4 = .75 hour at 70 ---> 52.5
1/6 = .167 hr at 95 ---> 15.8
1/2 = .5 hr at 55 ---> 27.5
20/60 = .333 hr at 0 --> 0
total time = 1.75 hours
total distance = 95.8 km
so
95.8 km / 1.75 hr = 54.7 km/hour
Thank you, I now understand it.
To solve this problem, you need to calculate the total distance traveled and the total time taken, and then divide the distance by the time to find the average speed.
Let's break down the problem step by step:
1. Convert the time durations into hours:
- 45.0 min = 45.0 / 60 = 0.75 hours
- 10.0 min = 10.0 / 60 = 0.1667 hours
- 30.0 min = 30.0 / 60 = 0.5 hours
- 20.0 min = 20.0 / 60 = 0.3333 hours
2. Calculate the distances traveled at each speed:
- Distance1 = Speed1 x Time1 = 70.0 km/h x 0.75 hours
- Distance2 = Speed2 x Time2 = 95 km/h x 0.1667 hours
- Distance3 = Speed3 x Time3 = 55.0 km/h x 0.5 hours
3. Calculate the total distance traveled:
- Total Distance = Distance1 + Distance2 + Distance3
4. Calculate the total time taken:
- Total Time = Time1 + Time2 + Time3 + 0.3333 hours (eating lunch and buying gas)
5. Calculate the average speed:
- Average Speed = Total Distance / Total Time
Now, let's calculate each step:
Step 1: Conversion of time durations to hours:
- 45.0 min = 0.75 hours
- 10.0 min = 0.1667 hours
- 30.0 min = 0.5 hours
- 20.0 min = 0.3333 hours
Step 2: Calculation of distances traveled at each speed:
- Distance1 = Speed1 x Time1 = 70.0 km/h x 0.75 hours = 52.5 km
- Distance2 = Speed2 x Time2 = 95 km/h x 0.1667 hours = 15.835 km
- Distance3 = Speed3 x Time3 = 55.0 km/h x 0.5 hours = 27.5 km
Step 3: Calculation of total distance traveled:
- Total Distance = Distance1 + Distance2 + Distance3 = 52.5 km + 15.835 km + 27.5 km = 95.835 km
Step 4: Calculation of total time taken:
- Total Time = Time1 + Time2 + Time3 + 0.3333 hours = 0.75 hours + 0.1667 hours + 0.5 hours + 0.3333 hours = 1.7499 hours
Step 5: Calculation of average speed:
- Average Speed = Total Distance / Total Time = 95.835 km / 1.7499 hours = 54.8 km/h (rounded to one decimal place)
So, the correct answer is approximately 54.8 km/h. Therefore, option c, 54.7 km/h, is the closest choice out of the given options.