Question

If a person travels at a speed of \(40\ \text{km/h}\) he will reach his destination on time. He covered half the journey in \(\frac{2}{3}\) of the time. At what speed (in km/h) should he travel to cover the remaining journey to reach the destination on time?

• A. \(48\)
• B. \(50\)
• C. \(60\)
• D. \(72\)

Hint:

Break the problem into parts: calculate the time used for the first segment, subtract from total allowed time, and use the remaining distance and time to find the required speed.

Answer 1

The Correct Option is C

Step 1: Represent the problem variables.
Let total distance = \(D\) km, Speed for on-time arrival = \(40\) km/h, So total time allowed = \(\frac{D}{40}\) hours.
Step 2: Time spent on first half.
First half distance = \(\frac{D}{2}\) km. Time used for first half = \(\frac{2}{3}\) of total time allowed: \[ t_1 = \frac{2}{3} \times \frac{D}{40} = \frac{D}{60} \ \text{hours}. \] Thus speed for first half = \(\frac{\frac{D}{2}}{\frac{D}{60}} = 30\) km/h.
Step 3: Time remaining.
Total allowed time = \(\frac{D}{40}\), time used = \(\frac{D}{60}\), so remaining time: \[ t_2 = \frac{D}{40} - \frac{D}{60} = \frac{3D - 2D}{120} = \frac{D}{120} \ \text{hours}. \] Step 4: Speed for second half.
Distance remaining = \(\frac{D}{2}\), time = \(\frac{D}{120}\), Speed needed = \(\frac{\frac{D}{2}}{\frac{D}{120}} = 60\) km/h. \[ \boxed{60\ \text{km/h}} \]