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Zorluk: ZorRatio, Proportion, and Rate

A delivery van travels from Town A to Town B, a distance of 120 km120\text{ km}, at an average speed of 60 km/h60\text{ km/h}. On the return journey along the same route, traffic congestion reduces its average speed by one-third. What is the average speed of the van for the entire round trip?

  1. 48 km/h48\text{ km/h}Cevap
  2. B
    50 km/h50\text{ km/h}
  3. C
    30 km/h30\text{ km/h}
  4. D
    24 km/h24\text{ km/h}

Cevap

The average speed for the entire round trip is 48 km/h48\text{ km/h}.
The correct answer is found by dividing the total round-trip distance of 240 km240\text{ km} by the total journey time of 5 hours5\text{ hours} (2 hours2\text{ hours} outbound and 3 hours3\text{ hours} return), yielding 48 km/h48\text{ km/h}.

Adım Adım Çözüm

1
Calculate the time taken for the outbound journey.
Timeout=120 km60 km/h=2 hours\text{Time}_{\text{out}} = \frac{120\text{ km}}{60\text{ km/h}} = 2\text{ hours}.
Time equals distance divided by speed.
2
Calculate the return speed and return time.
\text{Return speed} = 60 - \left(\frac{1}{3} \times 60\right) = 40\text{ km/h}. \text{Time}_{\text{return}} = \frac{120\text{ km}}{40\text{ km/h}} = 3\text{ hours}.
Speed reduction of one-third leaves two-thirds of the initial speed.
3
Compute total distance and total time for the round trip.
\text{Total distance} = 120 + 120 = 240\text{ km}; \text{Total time} = 2 + 3 = 5\text{ hours}.
A round trip covers the distance twice.
4
Divide total distance by total time to find average speed.
\text{Average speed} = \frac{240\text{ km}}{5\text{ hours}} = 48\text{ km/h}.
Average rate over unequal sub-intervals requires total quantity over total time.

Anahtar Kavram

Average Rate for Round-Trip Journeys
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Konular

Ratio, Proportion, and Rate

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