Emilio left Sunshine Road at 8:30 A.M. and arrived at Summer Lane at 1:30 P.M. His average speed for the whole journey was 60 km per hour. For the first 60% of the trip, he drove at an average speed at of 90 km per hour. For the next 25% of the remaining trip, his average speed was 60 km per hour. Find his average speed for the remaining part of the trip.
The average speed for the whole trip was 60 km/h
the total time is 5 hours, so the total distance = 300 km
time for first leg = .6(300)/90 = 2 hours
time for 2nd leg = .25(.4)(300)/60 = .5 hours
leaving him with 2.5 hours for the last part
distance he still has to go = 300 - .6(300) - .25(.4)(300) = 90 km
so speed for last leg = 90/2.5 = 36 km/h
plz show all of your work
thank you
Well, Emilio seems to be quite the speedster! Let's break down the information we have and find his average speed for the remaining part of the trip.
We know that Emilio drove at 90 km/h for 60% of the trip. So, for the first part of the trip, he was zooming along with the wind in his hair.
Next, we're told that for the next 25% of the remaining trip, his average speed was 60 km/h. This means that for that part of the journey, he must have hit some congestion or maybe took a pit stop for a snack.
Now, to find the average speed for the remaining part of the trip, we can subtract the distance covered in the first two parts from the total distance.
Assuming the total distance of the journey is X km, we can calculate the remaining distance as:
Remaining distance = X - (Distance covered in first part + Distance covered in second part)
Now, if we use the formula for average speed, which is: Average speed = Total distance / Total time, we can rearrange that to find the remaining time:
Remaining time = Remaining distance / Average speed for remaining part
And ta-da! We now know his average speed for the remaining part of the journey. I hope Emilio had a fantastic adventure on Sunshine Road and Summer Lane!
To find Emilio's average speed for the remaining part of the trip, we need to calculate the distance and time for the first and second parts of the journey and then subtract them from the total distance and time.
Let's start by calculating the distance and time for the first part of the journey, where Emilio drove at an average speed of 90 km/h for 60% of the total trip.
Total Distance for the first part:
Let's assume the total distance for the journey is D km.
So, the distance covered in the first part is 60% of D, which is 0.60D km.
Total Time for the first part:
Emilio left Sunshine Road at 8:30 A.M. and arrived at Summer Lane at 1:30 P.M. The total time for the journey is 1:30 P.M. - 8:30 A.M. = 5 hours.
Since Emilio drove at an average speed of 90 km/h for 60% of the total trip, we can find the time taken for the first part using the formula: Time = Distance / Speed -> Time = (0.60D km) / (90 km/h).
Now, let's calculate the distance and time for the second part of the journey, where Emilio drove at an average speed of 60 km/h for 25% of the remaining trip.
Remaining Distance:
The remaining distance is 100% - 60% = 40% of D, which is 0.40D km.
Remaining Time:
To calculate the remaining time, we first need to find the time taken for the first part of the journey and then subtract it from the total time.
The time taken for the first part is (0.60D km) / (90 km/h), as calculated before.
The remaining time for the journey is 5 hours - (0.60D km) / (90 km/h).
Now, let's calculate the total distance and time for the trip:
Total Distance = Distance for the first part + Remaining Distance
Total Time = Time for the first part + Remaining Time
Then, we can find the average speed for the remaining part of the trip by using the formula:
Average Speed = Total Distance / Total Time
By plugging in the respective values, we will get the answer.