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Two persons A and B start from the same point. A walks at 5 km/h. After 't' hours B starts and catches A after 2 hours of his own walking. If BтАЩs speed is 8 km/h, what is the value of 't'?
1.5
1.2
1.4
1.3
2
Equate distance: SAтАЛ├Ч(t+tBтАЛ)=SBтАЛ├ЧtBтАЛ. Since SAтАЛ(t+2)=SBтАЛ(2), we get 5(t+2)=16, so 5t=6, t=1.2.
Speed of A (SAтАЛ) = 5 km/h, Speed of B (SBтАЛ) = 8 km/h, time B walked (tBтАЛ) = 2 hours, time gap before B starts = t hours.
Distance=Speed├ЧTime
Equate distance: SAтАЛ├Ч(t+tBтАЛ)=SBтАЛ├ЧtBтАЛ. Since SAтАЛ(t+2)=SBтАЛ(2), we get 5(t+2)=16, so 5t=6, t=1.2.
Students often add t to 2 for person B's time instead of person A's, or confuse the total duration of the trip.
Calculate distance covered by B
Since B travels at 8 km/h for 2 hours, the total distance from the starting point is determined by B's speed and time.
D=8┬аkm/h├Ч2┬аh=16┬аkm
Determine total time for A
A has been walking for the initial delay t plus the 2 hours B took to catch up, meaning A's total time is (t+2) hours.
TimeAтАЛ=t+2
Equate distances to find t
Since A and B cover the same distance, set 5(t+2)=16. Solving for t: 5t+10=16, which implies 5t=6.
t=56тАЛ=1.2┬аhours
B is correct because the distance covered by A, 5(t+2), equated to B's distance of 16 km, yields t=1.2 hours.
This concept of equating distances is fundamental in 'Trains' and 'Circular Motion' problems where meeting points determine the time interval.
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