Solution:
Given:
Distance = 30 km
Amit's time is 2 hours more than Sameer's time.
Amit's time with double speed is 1 hour less than Sameer's time.
Concept used:
Distance = Speed × Time
Calculation:
Let, Sameeer's speed = s km/hr
Sameer's required time = 30/s hr
According to the question,
Amit's required time = 30/s + 2 = (30 + 2s)s hr
So, Amit's speed = 30 ÷ (30 + 2s)/s = 30s/(30 + 2s) km/hr
30 ÷ (2 × 30s/(30 + 2s)) = 30/s - 1
⇒ 30 ÷ 60s/(30 + 2s) = (30 - s)/s
⇒ (30 + 2s)/2s = (30 - s)/s
⇒ s × (30 + 2s) = 2s × (30 - s)
⇒ 30s + 2s2 = 60s - 2s2
⇒ 4s2 = 30s
⇒ s = 7.5 km/hr
So, Amit's speed = (30 × 7.5)/(30 + 2 × 7.5) = 5 km/hr
∴ Amit's original speed is 5 km/hr.
