Advertisements
Advertisements
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.
Advertisements
उत्तर
i. Speed of ordinary train = x km/hr
Speed of express train = (x + 25) km/hr
Distance = 300 km
We know
`"Time" = "Distance"/"Speed"`
∴ Time taken by ordinary train to cover 300 km = `300/x` hrs
Time taken by express train to cover 300 km = `300/(x + 25)` hrs
ii. Given that the ordinary train takes 2 hours more than the express train to cover the distance.
Therefore,
`300/x - 300/(x + 25) = 2`
`(300x + 7500 - 300x)/(x(x + 25)) = 2`
`7500 = 2x^2 + 50x`
`2x^2 + 50x - 7500 = 0`
`x^2 + 25x - 3750 = 0`
`x^2 + 75x - 50x - 3750 = 0`
`x(x + 75) - 50(x + 75) = 0`
`(x + 75)(x - 50) = 0`
x = –75, 50
But, speed cannot be negative.
So, x = 50.
∴ Speed of the express train = (x + 25) km/hr = 75 km/hr.
APPEARS IN
संबंधित प्रश्न
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
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 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.
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.
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.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:
- the onward journey;
- the return journey.
If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.
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.
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 a boat is 32 km/h. If the speed of stream is 8 km/h, the speed of boat upstream is ______.
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?
