QQuestion
A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more, it would have taken 1 hour less. Find x, the original speed.
ICSEClass 10MathematicsQuadratic Equations03 Mark2023 Easy
✓Answer
In the first case:
Distance = 100 km
Speed = x km/hr
⇒ Time taken = \frac{100}{x} hours
In the second case:
Speed = (x + 5) km/hr
⇒ Time taken = \frac{100}{x+5} hours
The faster journey takes 1 hour less.
⇒ \frac{100}{x}-\frac{100}{x+5}=1
⇒ \frac{100(x+5)-100x}{x(x+5)}=1
⇒ \frac{500}{x²+5x}=1
⇒ x² + 5x = 500
⇒ x² + 5x − 500 = 0
⇒ x² + 25x − 20x − 500 = 0
⇒ x(x + 25) − 20(x + 25) = 0
⇒ (x − 20)(x + 25) = 0
⇒ x = 20 or x = −25
Speed cannot be negative.
Therefore, the original speed is 20 km/hr.
Was this answer helpful?
Related Questions
More ICSE Easy level questions
1/12
If 3 is a root of the quadratic equation x2 − px + 3 = 0, then p is equal to: (a) 4 (b) 3 (c) 5 (d) 2
Solve the following quadratic equation: x2 + 4x − 8 = 0. Give your answer correct to one decimal place. Use mathematical tables if necessary.
The roots of the equation px² − qx + r = 0 are real and equal if: (a) p² = 4qr (b) q² = 4pr (c) −q² = 4pr (d) p² > 4qr
The difference of two natural numbers is 5 and sum of their reciprocals is . Find the two numbers.
Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.
Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0
The quadratic equation 3x² + √7x + 2 = 0 has: (a) two equal real roots. (b) two distinct real roots. (c) more than two real roots. (d) no real roots.
The nature of the roots of the equation 3x² − 6x − 3 = 0 is: (a) Real and equal (b) Real, distinct and rational (c) Real, distinct and irrational (d) No real roots
Mr and Mrs Das travelled by car from Delhi to Kasauli, a distance of approximately 350 km. Heavy rain reduced the average speed by 20 km/h and increased the journey time by 2 hours. Find: (a) the original speed of the car. (b) the time taken at the reduced speed.
Solve the quadratic equation (x − 2)² − 5x − 3 = 0 and give your answer correct to 3 significant figures.
The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term is 128. Find its: (a) common ratio (b) first term
Rohit and Vinay both opened a recurring deposit account in a bank for 2 years at 8% simple interest. Vinay deposited ₹ 300 per month. On maturity, Rohit’s interest was ₹ 800 more than Vinay’s interest. Find: (a) interest earned by Vinay. (b) sum deposited by Rohit every month.