Two friends 10 km apart start running towards each other at speeds of 10 km/hr and 14 km/hr respectively. After how much time will they meet each other?
- (a)20 minutes
- (b)25 minutes
- (c)28 minutes
- (d)30 minutes
Correct — B, 25 minutes. Two bodies approaching each other close the gap at the sum of their speeds, so the relative speed is 10 + 14 = 24 km/hr. The gap is 10 km, so the time to meet is 10 ÷ 24 = 5/12 of an hour. Multiply by 60 to convert: 5/12 × 60 = 25 minutes.
- (a)20 minutes — Twenty minutes is a third of an hour, which would need a closing speed of 30 km/hr. The two speeds add to 24, not 30.
- (c)28 minutes — This is close to the answer but not produced by any step; 10/24 of an hour is exactly 25 minutes, with no rounding involved.
- (d)30 minutes — Half an hour would need a closing speed of 20 km/hr — the figure you get by using only the average of the two speeds instead of their sum.
Relative speed converts a two-body problem into a one-body problem. Moving towards each other, the speeds add; moving in the same direction, they subtract. Once the closing speed is known, the meeting time is simply the initial gap divided by it.
The one thing to watch is units. Speeds are in kilometres per hour and the answer is wanted in minutes, so the hour figure of 5/12 has to be multiplied by 60 before it is compared with the options. Two further checks are available: the faster runner covers 14 × 5/12 ≈ 5.83 km and the slower 10 × 5/12 ≈ 4.17 km, and those add to exactly 10 km.
- Opposite directions: relative speed = sum of the speeds. Same direction: relative speed = difference.
- Time to meet = initial separation ÷ relative speed.
- To convert km/hr to m/s multiply by 5/18; to convert hours to minutes multiply by 60.
- The distances covered by the two bodies before meeting are in the ratio of their speeds — here 10 : 14, that is 5 : 7.
Add the speeds when the motion is towards each other; subtract them when it is in the same direction.
- Averaging the two speeds instead of adding them.
- Leaving the answer in hours when the options are in minutes.
- Subtracting the speeds, which is the rule for pursuit rather than for approach.
Asked as two bodies approaching or chasing each other with the meeting time, the meeting point or one of the speeds as the unknown.
Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other travels south at 40 kmph. After how many hours will the trains be 150 km apart?
- (a) 3/2
- (b) 15/4
- (c) 3/4
- (d) 15/2
Answer(a) 3/2
The same rule with the motion reversed — the trains open a gap instead of closing one, but because they move in opposite directions the speeds still add, to 100 km/hr, and 150 ÷ 100 gives the time.
- practice — not a real PYQ
Two cars 180 km apart move towards each other at 50 km/hr and 40 km/hr. They meet after
- (a)1 hour
- (b)1.5 hours
- (c)2 hours
- (d)2.5 hours
Answer(c) 2 hours — the closing speed is 90 km/hr, and 180 ÷ 90 = 2.
- practice — not a real PYQ
A thief running at 9 km/hr is chased by a policeman running at 12 km/hr. If the thief is 200 m ahead, the policeman catches him in
- (a)2 minutes
- (b)3 minutes
- (c)4 minutes
- (d)5 minutes
Answer(c) 4 minutes — same direction means the speeds subtract, giving 3 km/hr; 0.2 ÷ 3 hour is 1/15 hour, that is 4 minutes.