Advertisements
Advertisements
Question
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’.
Advertisements
Solution
We know
`"Time" = "Distance"/"Speed"`
Given, the girl covers a distance of 6 km at a speed x km/hr.
Time taken to cover first 6 km = `6/x`
Also, the girl covers the remaining 6 km distance at a speed (x + 2) km/hr.
Time taken to cover next 6 km = `6/(x + 2)`
Total time taken to cover the whole distance = 2 hrs 30 mins
= `2 30/60`
= `2 1/2`
= `5/2` hrs
`∴ 6/x + 6/(x + 2) = 5/2`
`(6x + 12 + 6x)/(x(x + 2)) = 5/2`
`(12 + 12x)/(x^2 + 2x) = 5/2`
24 + 24x = 5x2 + 10x
5x2 – 14x – 24 = 0
5x2 – 20x + 6x – 24 = 0
5x(x – 4) + 6(x – 4) = 0
(5x + 6)(x – 4) = 0
`x = (-6)/5, 4`
Since, speed cannot be negative.
Therefore, x = 4.
RELATED QUESTIONS
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.
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 ______.
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?
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 ______.
