When the speed of a truck is increased by 20%, it takes 25 minutes less to cover the same distance. What is the time (in hours) taken to cover twice the distance at its actual speed?
5
The correct answer is 5.
T_{\text{new}} = \frac{1}{1.2} T We also know T_{\text{new}} = T - 25. So: T - 25 = \frac{1}{1.2} T T - \frac{1}{1.2} T = 25 T \left(1 - \frac{1}{1.2}\right) = 25 T \left(1 - \frac{10}{12}\right) = 25 T \left(1 - \frac{5}{6}\right) = 25 T \left(\frac{6 - 5}{6}\right) = 25 T \left(\frac{1}{6}\right) = 25 T = 25 \times 6 = 150 minutes This confirms our earlier calculation for the original time T.
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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?
