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Zorluk: ZorAverage Speed

A military convoy must travel a total distance of 540540 miles to reach a forward operating base. To ensure they arrive on schedule, they need to maintain an overall average speed of 4545 miles per hour for the entire journey.

During the first segment, they travel 150150 miles in exactly 150150 minutes. During the second segment, they travel 135135 miles at an average speed of 3030 miles per hour.

What average speed, in miles per hour, must the convoy maintain for the remainder of the trip to meet their target overall average speed?

Cevap: 51 mph

Cevap

The convoy must maintain a speed of 51 mph for the remainder of the trip.
To find the required speed for the remainder of the trip, you must determine how much distance is left and how much time remains. First, calculate the total time allowed for the trip: 540 miles÷45 mph=12 hours540 \text{ miles} \div 45 \text{ mph} = 12 \text{ hours}. The first segment takes 150 minutes÷60=2.5 hours150 \text{ minutes} \div 60 = 2.5 \text{ hours} to cover 150150 miles. The second segment takes 135 miles÷30 mph=4.5 hours135 \text{ miles} \div 30 \text{ mph} = 4.5 \text{ hours}. The total distance covered so far is 285285 miles (150+135150 + 135) over a total of 77 hours (2.5+4.52.5 + 4.5). This leaves 255255 miles (540−285540 - 285) to be covered in the remaining 55 hours (12−712 - 7). Dividing the remaining distance by the remaining time (255÷5255 \div 5) results in a required speed of 5151 mph.

Adım Adım Çözüm

1
Calculate the total allowable time for the entire journey.
1212 hours
Total time is found by dividing the total distance (540540 miles) by the overall target average speed (4545 mph).
2
Convert the duration of the first segment into hours.
2.52.5 hours
To maintain consistent units, divide the given 150150 minutes by 6060 minutes per hour.
3
Calculate the time required for the second segment.
4.54.5 hours
Time equals distance divided by speed (135 miles÷30 mph135 \text{ miles} \div 30 \text{ mph}).
4
Determine the remaining distance and remaining time for the final segment.
Remaining distance: 255255 miles. Remaining time: 55 hours.
Subtract the completed distances (150+135=285150 + 135 = 285) from 540540, and subtract the used time (2.5+4.5=72.5 + 4.5 = 7) from 1212.
5
Calculate the required average speed for the final segment.
5151 miles per hour
Average speed equals remaining distance divided by remaining time (255÷5255 \div 5).

Anahtar Kavram

Average speed over multiple segments requires calculating total distance and total time, rather than taking the arithmetic mean of individual segment speeds.
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