Question

Rohan and Rahul are 144 km apart at A and B. Rohan travels at 8 km/hr. Rahul travels 4 km in the first hour, 5 km in the second, 6 km in the third, and so on. Find the point where they meet.

• A. 64 km from point A
• B. 64 km from point B
• C. Midway of A and B
• D. None of the above

Hint:

When one motion increases by 1 each hour, use the arithmetic series sum for distance: \(S_n=\frac{n}{2}(\text{first}+\text{last})\).

Answer 1

The Correct Option is C

Let they meet after \(t\) hours. Rohan covers \(8t\) km. Rahul covers \(4+5+\cdots+(3+t)=\dfrac{t}{2}(4+t+3)=\dfrac{t(t+7)}{2}\) km.
They meet when total \(=144\): \(8t+\dfrac{t(t+7)}{2}=144 \Rightarrow t^2+23t-288=0\). Solving gives \(t=9\) hours (positive root). Rohan’s distance \(=8\times 9=72\) km from A, which is half of 144; hence the meeting point is midway.