QQuestion
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.
✓Answer
Let the original speed be x km/h.
Distance = 350 km
Original time = \frac{350}{\mathrm{x}} hours
Reduced speed = (x − 20) km/h
Time at reduced speed = \frac{350}{\mathrm{x}-20} hours
The journey time increased by 2 hours:
⇒ \frac{350}{\mathrm{x}-20}-\frac{350}{\mathrm{x}}=2
⇒ \frac{350x-350(\mathrm{x}-20)}{\mathrm{x}(\mathrm{x}-20)}=2
⇒ \frac{7000}{\mathrm{x}(\mathrm{x}-20)}=2
⇒ x(x − 20) = 3,500
⇒ x² − 20x − 3,500 = 0
⇒ x² + 50x − 70x − 3,500 = 0
⇒ x(x + 50) − 70(x + 50) = 0
⇒ (x + 50)(x − 70) = 0
⇒ x = −50 or x = 70
Speed cannot be negative, so the original speed was 70 km/h.
Reduced speed = 70 − 20 = 50 km/h
Time at reduced speed = \frac{350}{50}
⇒ Time = 7 hours
Related Questions
More ICSE Hard level questions
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.
Solve the quadratic equation 2x² − 5x − 4 = 0. Give your answers correct to three significant figures.
Solve the following quadratic equation: x2 + 4x − 8 = 0. Give your answer correct to one decimal place. Use mathematical tables if necessary.
Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0
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
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.
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
Prove that:
Mrs Rao deposited ₹250 per month in a recurring deposit account for 3 years. She received ₹10,110 at maturity. Find: (a) the rate of interest. (b) how much more interest she would receive if she deposited ₹50 more per month at the same rate and for the same time.
X, Y, Z and C are points on the circumference of a circle with centre O. AB is a tangent to the circle at X and ZY = XY. Given ∠OBX = 32° and ∠AXZ = 66°, find: (a) ∠BOX (b) ∠CYX (c) ∠ZYX (d) ∠OXY
In △ABC, ∠ABC = 90°, AB = 20 cm and AC = 25 cm. DE is perpendicular to AC such that ∠DEA = 90° and DE = 3 cm, as shown. (a) Prove that △ABC ∼ △AED. (b) Find BC, AD and AE. (c) If BCED represents land on a map whose actual area is 576 m², find the scale factor of the map.
AB is a vertical tower 100 m from the foot of a 30-storey building CD. The angles of depression from C and E, where E is the midpoint of CD, are 35° and 14° respectively. Use mathematical tables, rounding required values to two decimal places. Find the height of: (a) tower AB. (b) building CD.