Advertisements
Advertisements
प्रश्न
A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.
Advertisements
उत्तर
Time taken by a man = `100/x` hrs.
Now, New speed of man = (x + 5) km/hr
∴ Time taken by a man = `100/((x + 5))` hrs.
According to question,
`100/x - 100/(x + 5)` = 1 hour
`100[1/x - 1/(x + 5)]` = 1
`100[(x + 5 - x)/(x(x + 5))]` = 1
500 = x(x + 5)
x2 + 5x – 500 = 0
x2 + 25x – 20x – 500 = 0
x(x + 25) – 20(x + 25) = 0
(x + 25)(x – 20) = 0
x = 20 or x = – 25 ...(Speed cannot be negative)
Hence x = 20 km/hour
संबंधित प्रश्न
The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr.
- Find the time taken by each train to cover 300 km.
- If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train.
If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.
The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate:
- the time taken by the car to reach town B from A, in terms of x;
- the time taken by the train to reach town B from A, in terms of x.
- If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
- Hence, find the speed of the train.
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each train.
Some school children went on an excursion by a bus to a picnic spot at a distance of 300 km. While returning, it was raining and the bus had to reduce its speed by 5 km/hr and it took two hours longer for returning. Find the time taken to return.
The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:
| Distance (in m) | 60 | 90 | y |
| Time (in sec) | 2 | x | 5 |
The values of x and y are:
A car travels a distance of 72 km at a certain average speed of x km per hour and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.
The speed of train A is x km/h and speed of train B is (x – 5) km/h. How much time will each train take to cover 400 km?
A car is moving with a speed of 100 km/h. If the speed of car first increases by x% and then decreases by x%, the final speed of the car is 96 km/h. The value of x is ______.
The speed of a boat in still water is 15 km/h and speed of stream is 5 km/h. The boat goes x km downstream and then returns back to the point of start is ______.
