A bus takes two hours less for a journey of 300 km, if its speed is increased…
2023
A bus takes two hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its normal speed. The normal speed is
Answer: B. 25 km/hr — CONCEPTFor a fixed distance, time equals distance divided by speed: t = d/v. When speed increases, the time saved is the difference between the original…
- A.
20 km/hr
- B.
25 km/hr
- C.
35 km/hr
- D.
50 km/hr
Show answer & explanation
Correct answer: B
CONCEPT
For a fixed distance, time equals distance divided by speed: t = d/v.
When speed increases, the time saved is the difference between the original travel time and the new travel time.
APPLICATION
Let the normal speed be x km/hr. The original time is 300/x hours, and the increased speed is (x + 5) km/hr.
The new time is 300/(x + 5) hours. Since 2 hours are saved, 300/x − 300/(x + 5) = 2.
Combining the fractions gives 1500/[x(x + 5)] = 2, so x(x + 5) = 750.
Thus x2 + 5x − 750 = 0 = (x − 25)(x + 30). A speed must be positive, so x = 25 km/hr.
CROSS-CHECK
At 25 km/hr, the journey takes 300/25 = 12 hours. At 30 km/hr, it takes 300/30 = 10 hours. The saving is 2 hours, as required.
Result: The normal speed is 25 km/hr.