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Math  /  Algebra

QuestionНисэх онгоцны буудал дээр 500 м урт урсдаг хэвтээ зам байжээ. Түүний хурд 4 км/ц бөгөөд Хүслэн, Нандиа хоёр энэ зам дээр хамт алхаж гарсан ба Хүслэн 6 км/ц хурдтай алхаж, Нандиа зүгээр зогссон бол зам дуусахад Хүслэн, Нандиагаас хэр холдсон байх вэ?

Studdy Solution

STEP 1

1. The moving walkway is 500 meters long.
2. The speed of the moving walkway is 4 km/h.
3. Khuslen walks at a speed of 6 km/h on the moving walkway.
4. Nandia stands still on the moving walkway.
5. We need to find the distance between Khuslen and Nandia when Khuslen reaches the end of the walkway.

STEP 2

1. Convert speeds from km/h to m/s.
2. Calculate the time it takes for Khuslen to reach the end of the walkway.
3. Calculate the distance traveled by Nandia in that same time.
4. Determine the distance between Khuslen and Nandia.

STEP 3

Convert speeds from km/h to m/s.
- The speed of the moving walkway is 4 km/h=4×10003600 m/s=109 m/s 4 \, \text{km/h} = \frac{4 \times 1000}{3600} \, \text{m/s} = \frac{10}{9} \, \text{m/s} . - Khuslen's walking speed is 6 km/h=6×10003600 m/s=53 m/s 6 \, \text{km/h} = \frac{6 \times 1000}{3600} \, \text{m/s} = \frac{5}{3} \, \text{m/s} .

STEP 4

Calculate the time it takes for Khuslen to reach the end of the walkway.
Khuslen's effective speed on the walkway is the sum of her walking speed and the walkway speed: Effective speed of Khuslen=53+109 m/s \text{Effective speed of Khuslen} = \frac{5}{3} + \frac{10}{9} \, \text{m/s}
Convert to a common denominator and add: 53=159 \frac{5}{3} = \frac{15}{9} Effective speed of Khuslen=159+109=259 m/s \text{Effective speed of Khuslen} = \frac{15}{9} + \frac{10}{9} = \frac{25}{9} \, \text{m/s}
Time to reach the end: Time=500259=500×925=180 seconds \text{Time} = \frac{500}{\frac{25}{9}} = \frac{500 \times 9}{25} = 180 \, \text{seconds}

STEP 5

Calculate the distance traveled by Nandia in that same time.
Nandia's speed is the same as the walkway's speed: Speed of Nandia=109 m/s \text{Speed of Nandia} = \frac{10}{9} \, \text{m/s}
Distance traveled by Nandia: Distance=109×180=200 meters \text{Distance} = \frac{10}{9} \times 180 = 200 \, \text{meters}

STEP 6

Determine the distance between Khuslen and Nandia.
Khuslen reaches the end of the 500-meter walkway, while Nandia has traveled 200 meters.
Distance between Khuslen and Nandia: Distance=500−200=300 meters \text{Distance} = 500 - 200 = 300 \, \text{meters}
The distance between Khuslen and Nandia when Khuslen reaches the end of the walkway is:
300 meters \boxed{300} \, \text{meters}

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