Advertisements
Advertisements
Question
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Advertisements
Solution
Let original speed be x km/hr.
∴ Time = `(72)/x "hr"`.
New speed = x + 10 km/hr.
∴ New time = `(72)/(x + 10)"hr".`
Difference in time = 36 mins.
∴ `(72)/x - (72)/(x + 10) = (36)/(60)`
`(72x + 720 - 72x)/(x(x + 10)) = (3)/(5)`
5 x 720 = 3 (x2 + 10x)
1,200 = x2 + 10x
x2 + 10x - 1,200 = 0
x2 + 40x - 30x - 1,200 = 0
x (x + 40) - 30 (x + 40) = 0
(x - 30) (x + 40) = 0
∴ x = 30
as x = -40 is not acceptable
∴ Original speed = 30km/hr.
RELATED QUESTIONS
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Solve for x : 12abx2 – (9a2 – 8b2 ) x – 6ab = 0
Divide 29 into two parts so that the sum of the squares of the parts is 425.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
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.
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.
