Advertisements
Advertisements
प्रश्न
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.
उत्तर
Time taken by a man = `100/x` hrs.
Now, New speed of man = (x + 5) km/hr
∴ Time taken by a man = `100/((x + 5))` hrs.
According to question,
`100/x - 100/(x + 5)` = 1 hour
`100[1/x - 1/(x + 5)]` = 1
`100[(x + 5 - x)/(x(x + 5))]` = 1
500 = x(x + 5)
x2 + 5x – 500 = 0
x2 + 25x – 20x – 500 = 0
x(x + 25) – 20(x + 25) = 0
(x + 25)(x – 20) = 0
x = 20 or x = – 25 ...(Speed cannot be negative)
Hence x = 20 km/hour
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.
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 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.
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 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.
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 ______.
