A and B start at 7:10 a.m. from two places and walk towards each other. After meeting, A takes 80 minutes and B takes 20 minutes to reach the other's starting point. At what time do they meet?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7:50 a.m.
The part A walks before the meeting is walked by B after it, and the other way round. This gives the time to the meeting directly.
Let them meet after \(t\) minutes, with speeds \(a\) and \(b\)
A's part before the meeting \(at=20b\); B's part before the meeting \(bt=80a\)
Multiplying: \(ab\,t^{2}=1600\,ab\), so \(t^{2}=80\times20=1600\) and \(t=40\) minutes
7:10 a.m. \(+\) 40 minutes \(=\) 7:50 a.m.
They meet at 7:50 a.m.