Advertisements
Advertisements
Question
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Advertisements
Solution
Let the original speed of train be x km/hr. Then,
Increased speed of the train = (x + 15)km/hr
Time taken by the train under usual speed to cover 90 km = `90/x`hr
Time taken by the train under increased speed to cover 90 km = `90/(x+15)`hr
Therefore,
`90/x-90/(x+15)=30/60`
`(90(x+15)-90x)/(x(x+15))=1/2`
`(90x+1350-90x)/(x^2+15x)=1/2`
`1350/(x^2+15x)=1/2`
1350(2) = x2 + 15x
2700 = x2 + 15x
x2 + 15x - 2700 = 0
x2 - 45x + 60x - 2700 = 0
x(x - 45) + 60(x - 45) = 0
(x - 45)(x + 60) = 0
So, either
x - 45 = 0
x = 45
Or
x + 60 = 0
x = -60
But, the speed of the train can never be negative.
Hence, the original speed of train is x = 45 km/hr
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`10x-1/x=3`
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Determine two consecutive multiples of 3, whose product is 270.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Solve the following quadratic equations by factorization:
`100/x-100/(x+5)=1`
Find two consecutive multiples of 3 whose product is 648.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
If the product of two positive consecutive even integers is 288, find the integers.
The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
