Multiple choice

Tarun can cover a certain distance in $1$ hr $24$ min by covering $\displaystyle \frac{2}{3}$ of the distance at $4$ km/hr and the rest at $5$ km/hr. The total distance is:

  1. $5$ km
  2. $6$ km
  3. $8$ km
  4. $9.2$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be D. Time = 1 hr 24 min = 1.4 hours. (2/3)D / 4 + (1/3)D / 5 = 1.4. D/6 + D/15 = 1.4. (5D + 2D) / 30 = 1.4 => 7D = 42 => D = 6.

AI explanation

Let the total distance be d km, so two-thirds of the distance is 2d/3 and the rest is d/3. The total time in hours is 1 hour 24 minutes converted to a decimal, which is 1.4 hours. The time equation is (2d/3)/4 + (d/3)/5 = 1.4. Solving this equation yields d/6 + d/15 = 1.4, so 7d/30 equals 1.4, which gives a total distance of 6 km.

Keep practicing — related questions