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Zorluk: OrtaAverage Speed

An engineer battalion is transporting heavy equipment in a convoy to a forward operating base 210210 miles away. To arrive on schedule, the convoy must maintain an overall average speed of 4242 mph for the entire journey.

During the first leg, the convoy travels 120120 miles in 22 hours. They then halt for 3030 minutes to inspect the equipment.

What average speed must the convoy maintain for the remainder of the trip to achieve the target overall average speed?

  1. A
    24 mph
  2. B
    30 mph
  3. 36 mphCevap
  4. D
    60 mph

Cevap

The convoy must maintain an average speed of 36 mph for the remainder of the trip.
To achieve an overall average speed of 4242 mph over 210210 miles, the total journey must take exactly 55 hours. The convoy has already used 2.52.5 hours (22 hours driving + 0.50.5 hours resting) and covered 120120 miles. This leaves 9090 miles to be covered in the remaining 2.52.5 hours. Dividing the remaining distance by the remaining time (90/2.590 / 2.5) gives the required speed of 3636 mph.

Adım Adım Çözüm

1
Calculate the total time required for the entire journey.
Total Time = 210 miles/42 mph=5 hours210 \text{ miles} / 42 \text{ mph} = 5 \text{ hours}.
To find the time available for the second leg, we first need to know the total time allowed for the mission.
2
Calculate the time spent on the first leg and the rest stop.
Time Spent = 2 hours+30 minutes=2.5 hours2 \text{ hours} + 30 \text{ minutes} = 2.5 \text{ hours}.
The rest stop must be included in the total elapsed time because the overall average speed accounts for the entire duration of the journey.
3
Determine the remaining distance and remaining time for the final leg.
Remaining Distance = 210−120=90 miles210 - 120 = 90 \text{ miles}.
Remaining Time = 5−2.5=2.5 hours5 - 2.5 = 2.5 \text{ hours}.
Subtracting the distance already covered and the time already spent gives the parameters for the final segment.
4
Calculate the required average speed for the final leg.
Speed = 90 miles/2.5 hours=36 mph90 \text{ miles} / 2.5 \text{ hours} = 36 \text{ mph}.
Average speed is always calculated as total distance divided by total time for that specific segment.

Anahtar Kavram

To find a missing speed in a multi-leg journey, use the total distance and target average speed to find the total allowed time. Subtract the time and distance already used (including rest stops) to find the parameters for the remaining leg.

Alternatif Yöntem

You can work entirely in minutes to avoid decimals. Total time is 300300 minutes. Time spent is 150150 minutes. Time remaining is 150150 minutes. Speed needed is 90 miles/150 minutes=0.6 miles per minute90 \text{ miles} / 150 \text{ minutes} = 0.6 \text{ miles per minute}. Multiply by 6060 to convert to 3636 mph.
Tahmini Süre:1m 30s
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Average Speed

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