Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the speed of the car be x km/hr.
Distance = 36 km
Time taken to cover a distance of 36 km = 36/x hrs
`("Time" = "Distance"/"Speed")`
New speed of the car = (x + 10) km/hr
New time taken by the car to cover a distance of 36 km = `36/(x + 10)` hrs
From the given information, we have:
`36/x - 36/(x + 10) = 18/60`
`(36(x + 10) - 36x)/(x(x + 10)) = 3/10`
`(36x + 360 - 36x)/(x(x + 10)) = 3/10`
`360/(x(x + 10)) = 3/10`
3x2 + 30x = 3600
3x2 + 30x – 3600 = 0
x2 + 10x – 1200 = 0 ...(Dividing by 3)
x2 + 40x – 30x – 1200 = 0
x(x + 40) – 30(x + 40) = 0
(x + 40)(x – 30) = 0
x = – 40, 30
But speed cannot be negative.
So, x = 30.
Hence, the original speed of the car is 30 km/hr.
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.
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.
A plane left 30 minutes later than the schedule time and in order to reach its destination 1500 km away in time, it has to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
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’.
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.
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 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 ______.
