Q10
Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is
Answer: D
Key idea: Use the first part to fix the starting terms of both progressions, then use total time and total distance.
- First part: speed \(960\) m/min \(=57.6\) km/h, time \(30\) min \(=\frac12\) h, distance 28.8 km.
- Times in AP: \(\frac12,\frac12+d,\frac12+2d,\frac12+3d\) with sum \(2+6d=3\Rightarrow d=\frac16\). Times: \(\frac12,\frac23,\frac56,1\) h.
- Speeds in AP: \(57.6+je\) for \(j=0,1,2,3\). Total distance:
\(57.6\left(\frac12+\frac23+\frac56+1\right)+e\left(\frac23+\frac{10}{6}+3\right)=224\)
\(172.8+\frac{16}{3}e=224\Rightarrow e=9.6\). - Fourth part: speed \(57.6+28.8=86.4\) km/h for 1 h, i.e. 86.4 km \(=86400\) m.
Check: distances 28.8, 44.8, 64, 86.4 km add up to 224 km.
Hence, the answer is (D) 86400.