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Zorluk: ZorRatios, Rates, and Proportions

A courier uses three modes of transportation to deliver packages: a bicycle, an electric scooter, and a delivery van. The ratio of the average speed of the electric scooter to the average speed of the bicycle is 3:23:2, and the ratio of the average speed of the delivery van to the average speed of the electric scooter is 5:25:2. If it takes the courier 6060 minutes to complete a delivery route using the bicycle, how many minutes would it take the courier to complete the exact same delivery route using the delivery van, assuming all average speeds remain constant?

  1. 16Cevap
  2. B
    24
  3. C
    36
  4. D
    100
  5. E
    225

Cevap

16 minutes
Because travel time is inversely proportional to speed when distance is constant, the time required decreases as speed increases. With a scooter-to-bicycle speed ratio of 3:23:2, the scooter takes 23\frac{2}{3} of the bicycle's time: 60×23=4060 \times \frac{2}{3} = 40 minutes. With a van-to-scooter speed ratio of 5:25:2, the van takes 25\frac{2}{5} of the scooter's time: 40×25=1640 \times \frac{2}{5} = 16 minutes.

Adım Adım Çözüm

1
Determine the relationship between the speed of the bicycle and the speed of the electric scooter.
vscooter=32vbicyclev_{\text{scooter}} = \frac{3}{2}v_{\text{bicycle}}
The given ratio of the average speed of the scooter to the bicycle is 3:23:2.
2
Calculate the time it would take to complete the route using the electric scooter.
4040 minutes
Since speed and travel time are inversely proportional for a constant distance, the scooter's time is 60×23=4060 \times \frac{2}{3} = 40 minutes.
3
Determine the relationship between the speed of the electric scooter and the delivery van.
vvan=52vscooterv_{\text{van}} = \frac{5}{2}v_{\text{scooter}}
The given ratio of the average speed of the van to the scooter is 5:25:2.
4
Calculate the time it would take to complete the route using the delivery van.
1616 minutes
Since speed and travel time are inversely proportional, the van's time is 40×25=1640 \times \frac{2}{5} = 16 minutes.

Anahtar Kavram

Inverse proportionality in rate-time-distance relationships and compounding multiple ratios
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Konular

Ratios, Rates, and Proportions

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