Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the original speed of the aeroplane be x km/hr.
Time taken to cover a distance of 1200 km = 1200/x hrs
`("Time" = "Distance"/"Speed")`
Let the new speed of the aeroplane be (x – 40) km/hr
Time taken to cover a distance of 1200 km = `1200/(x - 40)` hrs
From the given information, we have
`1200/(x - 40) - 20/60 = 1200/x`
`1200/(x - 40) - 1200/x = 20/60`
`(1200x - 1200x + 48000)/(x(x - 40)) = 1/3`
x(x – 40) = 48000 × 3
x2 – 40x – 144000 = 0
x2 – 400x + 360x – 144000 = 0
x(x – 400) + 360(x – 400) = 0
(x – 400)(x + 360) = 0
x = 400, – 360
But, speed cannot be negative.
So, x = 400.
Thus, the original speed of the aeroplane is 400 km/hr.
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 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 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’.
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.
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels 5 km/hr faster than the second train. If after 2 hours, they are 50 km apart, find the speed of each 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’.
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 is 32 km/h. If the speed of stream is 8 km/h, the speed of boat upstream is ______.
