A person travels equal distances at speeds of 3 km/h, 4 km/h, 7 km/h and 12km/h, and takes a total of 680 minutes. What is the total distance (in km) travelled?
56
The correct answer is 56.
\[ \text{Total Distance} = \frac{84}{17} \text{ km/h} \times \frac{34}{3} \text{ hours} \] \[ \text{Total Distance} = \frac{84}{17} \times \frac{34}{3} = \frac{84 \times 34}{17 \times 3} \] We can cancel terms: 34 is 2 \times 17, and 84 divided by 3 is 28. \[ \text{Total Distance} = \frac{28 \times (2 \times 17)}{17 \times 3} = \frac{28 \times 2}{1} = 56 \text{ km} \] This confirms the result obtained by summing individual times. Understanding average speed provides an alternative approach to solve problems involving equal distances travelled at different speeds.
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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?
