Emilio left Main Road at 8 A.M and arrived at Lame Lane at 2 P.M. His average for the whole journey was 60 mph. For the first 70% of the trip, he drove at an average speed of 65 mph. For the next 25% of the remaining trip, his average was 54 mph. Find his average speed for the remaining part of the trip.
Since it took him 6 hrs at 60 mph, I got 360 mi for how far it was and 70% of 360 is 252 and 25% is 90 which means the remaining part is 18. I don't know what to do with the 65 and 54.
he drove for 6 hours at 60 mph, or 360 miles
70% of 360 = 252
25% of 108 = 27
360-(252+27) = 81
since time = distance/speed,
252/65 + 27/54 + 81/x = 6
x = 10530/211 ≈ 49.9 mph
To solve this problem, we can break it down into steps:
Step 1: Calculate the total distance of the trip
- Since Emilio traveled at an average speed of 60 mph for a total of 6 hours, we can use the formula: distance = speed * time.
- Therefore, the total distance is 60 mph * 6 hours = 360 miles.
Step 2: Calculate the distance traveled during the first 70% of the trip
- We know that Emilio traveled at an average speed of 65 mph for this portion of the trip.
- To find the distance traveled during the first 70%, we can use the formula: distance = percentage * total distance.
- So, the distance traveled during the first 70% of the trip is 0.70 * 360 miles = 252 miles.
Step 3: Calculate the distance traveled during the next 25% of the remaining trip
- After completing the first 70% of the trip, there is still 30% of the trip remaining.
- Emilio traveled at an average speed of 54 mph for the next 25% of the remaining trip.
- To find the distance traveled during this portion, we can use the formula: distance = percentage * distance remaining.
- The distance remaining is 360 miles - 252 miles = 108 miles.
- Therefore, the distance traveled during the next 25% of the remaining trip is 0.25 * 108 miles = 27 miles.
Step 4: Calculate the remaining distance
- We know that the total distance is 360 miles, and the first 70% (252 miles) and next 25% (27 miles) have already been accounted for.
- Therefore, the remaining distance is 360 miles - 252 miles - 27 miles = 81 miles.
Step 5: Calculate the average speed for the remaining part of the trip
- Now that we have the remaining distance (81 miles), we can find Emilio's average speed for the remaining part of the trip.
- We know the remaining part represents the remaining 5% of the total trip (100% - 70% - 25% = 5%).
- Given that the remaining distance is 81 miles and the remaining portion is 5%, we can use the formula: average speed = distance / time.
- Therefore, the average speed for the remaining part of the trip is 81 miles / 5% = 81 miles / 0.05 = 1620 mph.
So, Emilio's average speed for the remaining part of the trip is 1620 mph.