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Two people drive towards each other from two places which are 56┬аkm apart. The speed of the first person is 12┬аkm/h and speed of the other is 13┬аkm/h. After how long will they be 6┬аkm apart if they start driving together?
1 hour 30 minutes
2 hours
1 hour
2 hours 10 minutes
2 hours
Calculate the effective distance they need to cover (56 - 6 = 50 km) and divide by their combined speed (12 + 13 = 25 km/h). 50 / 25 = 2 hours.
Total distance D = 56 km. Speed of first person v1 = 12 km/h. Speed of second person v2 = 13 km/h. Desired remaining distance d = 6 km.
t=v1+v2DтИТdтАЛ
Calculate the effective distance they need to cover (56 - 6 = 50 km) and divide by their combined speed (12 + 13 = 25 km/h). 50 / 25 = 2 hours.
Confusing the distance traveled with the remaining distance; many students calculate the time taken to meet (56 / 25) instead of the time to be 6 km apart.
Calculate relative speed
Since the people are moving towards each other, their relative speed is the sum of their individual speeds.
vrelтАЛ=12+13=25┬аkm/h
Determine distance to be covered
They start 56 km apart and need to be 6 km apart. The distance they must cover relative to each other is 56тИТ6=50 km.
DeffтАЛ=56тИТ6=50┬аkm
Calculate time
Using the formula for time, divide the effective distance by the relative speed.
t=2550тАЛ=2┬аhours
B is correct because the time taken to cover the net distance of 50 km at a relative speed of 25 km/h is exactly 2 hours.
This concept is a precursor to train crossing problems, where you must account for the sum of lengths in addition to distance.
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