Advertisements
Advertisements
प्रश्न
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
उत्तर
The distance between Akola and Bhusawal is 168 km.
Suppose, average speed of passenger train is x km/hr.
∴ the average speed of express train is (x + 14) km/hr.
∴ the time required for passenger train = `168/x` hours
and the time required for express train = `168/(x+14)` hours
∴ from the given condition,
`168/x-168/x+14=1`
∴` (168x+168xx14-168x)/(x(x+14))=1`
∴` x^2+14x=168xx14`
∴` x^2+14x-2352=0`
∴`x(x+56)-42(x+56)=0`
∴`x(x+56)-42(x-42)=0`
∴` x+56=0 or x-42=0`
∴` x=-56 or x=42`
But speed is not negative
`x=42`
∴ average speed of passenger train =42 km/hr
and average speed of express train =(42+14)=56 km/hr.
APPEARS IN
संबंधित प्रश्न
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
Two numbers differ by 3 and their product is 504. Find the number
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
`8x^2-14x-15=0`
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
