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: Understanding the Concept:
Total distance is the sum of distances covered in segments. Use speed \(\times\) time.
Step 2: Key Formula or Approach:
\( D = S_1 T_1 + S_2 T_2 + S_3 T_3 \). Ensure time is in hours.
Step 3: Detailed Explanation:
Total distance = 39. Total time = 45 min.
1. Part 1: T = 15/60 = 1/4 hr. S = x. \( D_1 = x/4 \).
2. Part 2: T = 20/60 = 1/3 hr. S = 2x. \( D_2 = 2x/3 \).
3. Part 3: T = (45 - 15 - 20) = 10 min = 1/6 hr. S = x. \( D_3 = x/6 \).
Sum: \( x/4 + 2x/3 + x/6 = 39 \).
LCM 12: \( \frac{3x + 8x + 2x}{12} = 39 \implies \frac{13x}{12} = 39 \implies x = 3 \times 12 = 36 \).
Step 4: Final Answer:
x is 36.