A person travels equal distances at speeds of 2 km/h, 4 km/h, 5 km/h, 7 km/h and 12 km/h, and takes a total of 1485 minutes. What is the total distance (in km) travelled (to the nearest integer)?
105
The correct answer is 105.
So, \frac{5}{V_{avg}} = \frac{494}{420} = \frac{247}{210} V_{avg} = \frac{5 \times 210}{247} = \frac{1050}{247} km/h. Total Distance = Average Speed \times Total Time Total Distance = \frac{1050}{247} \times \frac{99}{4} km Let's check if this matches our previous result: \frac{1050 \times 99}{247 \times 4} = \frac{103950}{988} Is \frac{103950}{988} equal to \frac{51975}{494}? Yes, because \frac{103950}{988} = \frac{51975 \times 2}{494 \times 2} = \frac{51975}{494}. So, the average speed approach also leads to the same total distance calculation, confirming our result.
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Important Questions from Relative Speed
- Ankur jogs on a circular track X at $1 \frac{2}{3}$ m/s and Mahima jogs on track Y at $2 \frac{1}{12}$ m/s. The total length of Tracks X and Y is 0.325 km. Ankur makes 9 rounds of track X in the same time Mahima makes 5 rounds of track Y. The time taken (in seconds) by Mahima to complete one round of track X is:
- Two places, A and B are 3710 kms from each other. A train leaves from A to B at the same time another train leaves B to A. The two trains meet at the end of 35 hours. If the train travelling from A to B travels 35 kmph faster than the other. Find the speed of the faster train. (In kmph)
- A truck, 1575 metres long is running at a speed of 109 km/hr. How many seconds will it take to cross a 1475 metres long train running in the same direction at a speed of 79 km/hr?
- A truck, 1600 metres long is running at a speed of 112 km/hr. How many seconds will it take to cross a 1500 metres long train running in the same direction at a speed of 82 km/hr?
- Two friends 10 km apart start running towards each other at speeds of 10 km/hr and 14 km/hr respectively. After how much time will they meet each other?
