Question

A motorist covers a distance of 39 km in 45 minutes by moving at a speed of x kmph for the first 15 minutes, then moving at a double the speed for the next 20 minutes and then again moving at his original speed for the rest of the journey. Then, x is equal to:

• A. 31.2
• B. 32
• C. 36
• D. 39.6
• E. 52

Hint:

Convert all times to hours and use distance = speed × time.

Answer 1

The Correct Option is C

Step 1: Total time = 45 minutes = $\frac{45}{60} = \frac{3}{4}$ hour.
Step 2: First part: time = 15 min = $\frac{1}{4}$ hour, speed = x kmph, distance = $\frac{x}{4}$ km.
Step 3: Second part: time = 20 min = $\frac{1}{3}$ hour, speed = 2x kmph, distance = $\frac{2x}{3}$ km.
Step 4: Third part: time = $45 - (15+20) = 10$ min = $\frac{1}{6}$ hour, speed = x kmph, distance = $\frac{x}{6}$ km.
Step 5: Total distance = $\frac{x}{4} + \frac{2x}{3} + \frac{x}{6} = 39$.
Step 6: Common denominator 12: $\frac{3x}{12} + \frac{8x}{12} + \frac{2x}{12} = \frac{13x}{12} = 39$.
Step 7: $13x = 468 \implies x = 36$.
Step 8: Final Answer: 36.