Ronald made a trip of 450 miles in 8 hours. Before noon he avg. 60 miles per hour, and after noon he avg. 50 miles per hour. At what time did he begin his trip and when did it end?
D=RT
450=60(8-x)+50x
Thank you so much for the equation - can u explain why we minus the 8 by x. I know it's the amount of time, can u clarify... thanks again
If I told you Ronald traveled 3 hours after noon, how long did he traveled before noon (given he traveled both before and after noon in 8 hours)?
5 hours
That is why it is 8-x. Do you understand?
yes i do now - thank you again - i can go to sleep now!! bye thanks
To find out when Ronald began and ended his trip, we need to analyze the given information.
We know that Ronald traveled a total of 450 miles in 8 hours. Let's break down his journey into two parts: before noon and after noon.
Before noon:
The average speed before noon was 60 miles per hour.
Let's use the formula: Distance = Speed × Time
Let the time before noon be x hours.
So the distance traveled before noon would be (60 miles per hour) × (x hours) = 60x miles.
Afternoon:
The average speed after noon was 50 miles per hour.
The total time for the trip was 8 hours, and we already accounted for x hours before noon. Therefore, the time after noon would be (8 - x) hours.
The distance traveled after noon would be (50 miles per hour) × (8 - x hours) = 50(8 - x) miles.
To find the total distance of the trip, we add the distances before and after noon:
60x + 50(8 - x) = 450
Now we can solve this equation to determine the time Ronald started his trip (x hours) and when he ended (8 - x hours).
Let's solve the equation step by step:
60x + 50(8 - x) = 450
Distribute:
60x + 400 - 50x = 450
Combine like terms:
10x + 400 = 450
Subtract 400 from both sides:
10x = 50
Divide by 10:
x = 5
The value of x is 5, which represents the time (in hours) before noon. Therefore, Ronald began his trip 5 hours before noon. Since the total duration of the trip is 8 hours, he ended his trip (8 - 5) = 3 hours after noon.
To convert these hours into a standard time format, we need to know the reference point for noon. Assuming noon is 12:00 PM, Ronald began his trip at 7:00 AM (5 hours before noon) and ended it at 3:00 PM (3 hours after noon).
So, Ronald began his trip at 7:00 AM and ended it at 3:00 PM.