Advertisements
Advertisements
प्रश्न
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Advertisements
उत्तर
Let the usual speed of aero plane be x km/hr. Then,
Increased speed of the aero plane = (x + 250) km/hr
Time taken by the aero plane under usual speed to cover 1250 km = `1250/x`hr
Time taken by the aero plane under increased speed to cover 1250 km = `1250/(x +250)`hr
Therefore,
`1250/x-1250/(x+250)=50/60`
`(1250(x+250)-1250x)/(x(x+250))=5/6`
`(1250x+312500-1250x)/(x^2+250x)=5/6`
`312500/(x^2+250x)=5/6`
312500(6) = 5(x2 + 250x)
1875000 = 5x2 + 1250x
5x2 + 1250x - 1875000 = 0
5(x2 + 250x - 375000) = 0
x2 + 250x - 375000 = 0
x2 - 500x + 750x - 375000 = 0
x(x - 500) + 750(x - 500) = 0
(x - 500)(x + 750) = 0
So, either
x - 500 = 0
x = 500
Or
x + 750 = 0
x = -750
But, the speed of the aero plane can never be negative.
Hence, the usual speed of train is x = 500 km/hr.
APPEARS IN
संबंधित प्रश्न
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
Divide 29 into two parts so that the sum of the squares of the parts is 425.
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
`x^2-4x+1=0`
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
