Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let x km/h be the original speed of the car.
We know that,
Time taken = `"Distance"/"Speed"`
It is given that the car covers a distance of 400 km with the speed of x km/h.
Thus, the time taken by the car to complete 400 km is t = `400/x`
Now, the speed is increased by 12 km.
Increased speed = (x + 12) km/h
Also given that, increasing the speed of the car will decrease the time taken by 1 hour 40 minutes.
Hence,
`400/x - 400/(x + 12)` = 1 hour 40 minutes
`=> 400/x - 400/(x + 12)` = `1 40/60`
`=> (400(x + 12) - 400x)/(x(x + 12)) = 1 2/3`
`=> (400x + 4800 - 400x)/(x(x + 12)) = 5/3`
`=> 4800/(x(x + 12)) = 5/3`
`=>` 3 × 4800 = 5 × x × (x + 12)
`=>` 14400 = 5x2 + 60x
`=>` 5x2 + 60x – 14400 = 0
`=>` x2 + 12x – 2880 = 0
`=>` x2 + 60x – 48x – 2880 = 0
`=>` x(x + 60) – 48(x + 60) = 0
`=>` (x + 60)(x – 48) = 0
`=>` x + 60 = 0 or x – 48 = 0
`=>` x = – 60 or x = 48
Since, speed cannot be negative, we reject – 60.
Hence, the original speed of the car is 48 km/h.
APPEARS IN
RELATED QUESTIONS
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 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.
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.
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 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 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?
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 ______.
