Advertisements
Advertisements
प्रश्न
A goods train leaves a station at 6 p.m., followed by an express train which leaved at 8 p.m. and travels 20 km/hour faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the train remain constant between the two stations; calculate their speeds.
Advertisements
उत्तर
Let the speed of goods train be x km/hr.
So, the speed of express train will be (x + 20) km/hr.
Distance = 1040 km
We know
Time = `"Distance"/"Speed"`
Time taken by good train to cover a distance of 1040 km = `1040/x` hrs
Time taken by express train to cover a distance of 1040 km = `1040/(x + 20)` hrs
It is given that the express train arrives at a station 36 minutes before the goods train. Also the express train leaves the station 2 hours after the goods train. This means that the express train arrives at the station `(36/60 + 2) "hrs" = 13/5 "hrs"` before the good train.
Therefore, we have
`1040/x - 1040/(x + 20) = 13/5`
`(1040x + 20800 - 1040x)/(x(x + 20)) = 13/5`
`20800/(x^2 + 20x) = 13/5`
`1600/(x^2 + 20x) = 1/5`
x2 + 20x – 8000 = 0
(x – 80)(x + 100) = 0
x = 80, –100
Since, the speed cannot be negative.
So, x = 80.
Thus, the speed of goods train is 80 km/hr and the speed of express train is 100 km/hr.
संबंधित प्रश्न
If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.
A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.
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.
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.
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.
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:
The speed of a boat is 32 km/h. If the speed of stream is 8 km/h, the speed of boat upstream is ______.
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 ______.
