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Zorluk: OrtaAlgebraic Word Problems and Modeling

Courier A departs from Warehouse X heading toward Warehouse Y at 8:00 AM traveling at a constant speed of 4040 miles per hour. Courier B departs from Warehouse Y heading toward Warehouse X along the same straight route at 9:00 AM traveling at a constant speed of 6060 miles per hour. If the total distance between Warehouse X and Warehouse Y is 190190 miles, at what time will the two couriers meet?

  1. A
    9:54 AM
  2. B
    10:00 AM
  3. 10:30 AMCevap
  4. D
    11:00 AM
  5. E
    11:15 AM

Cevap

10:30 AM
The correct answer is 10:30 AM. Between 8:00 AM and 9:00 AM, Courier A travels 40 miles alone. At 9:00 AM, the distance remaining between them is 150 miles. Because they travel toward each other, their speeds combine to 100 mph (40 + 60). Dividing 150 miles by 100 mph gives 1.5 hours (1 hour and 30 minutes). Adding 1 hour and 30 minutes to 9:00 AM gives a meeting time of 10:30 AM.

Adım Adım Çözüm

1
Calculate the distance traveled by Courier A before Courier B starts moving.
From 8:00 AM to 9:00 AM (1 hour), Courier A travels 40 mph×1 hour=40 miles40 \text{ mph} \times 1 \text{ hour} = 40 \text{ miles}.
Courier A has a 1-hour head start.
2
Determine the remaining distance to be covered between the two couriers at 9:00 AM.
Remaining distance =190−40=150 miles= 190 - 40 = 150 \text{ miles}.
Subtract Courier A's distance from the total distance of 190 miles.
3
Calculate the combined rate of both couriers and solve for elapsed time after 9:00 AM.
Combined rate =40+60=100 mph= 40 + 60 = 100 \text{ mph}. Elapsed time t=150100=1.5 hours=1 hour 30 minutest = \frac{150}{100} = 1.5 \text{ hours} = 1 \text{ hour } 30 \text{ minutes}.
Since they move toward each other, their speeds add up to close the gap.
4
Add the elapsed combined time to 9:00 AM to find the meeting time.
9:00 AM +1 hour 30 minutes=10:30 AM+ 1 \text{ hour } 30 \text{ minutes} = 10:30 \text{ AM}.
The combined movement began at 9:00 AM when Courier B started traveling.

Anahtar Kavram

Distance-rate-time relationship with staggered start times
Tahmini Süre:1m 30s
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Algebraic Word Problems and Modeling

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