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.
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
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