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Two people drive towards each other from two places which are 56 km apart. The speed of the first person is 12 km/h and the speed of the other is 14 km/h. After how long will they be 4 km apart if they start driving at the same time?
1 hour 30 minutes
1 hour
2 hours 10 minutes
2 hours
2 hours
Use relative speed towards each other. The total distance covered by both people to leave 4 km between them is 56−4=52 km. Divide by the sum of speeds 12+14=26 km/h.
Distance between two places = 56 km, Speed of first person (v1) = 12 km/h, Speed of second person (v2) = 14 km/h, Required distance between them = 4 km
t=v1+v2Initial Distance−Remaining Distance
Use relative speed towards each other. The total distance covered by both people to leave 4 km between them is 56−4=52 km. Divide by the sum of speeds 12+14=26 km/h.
Confusing the distance remaining between them with the total distance they travel. They only need to cover 56−4=52 km together.
Identify Relative Speed
Since both persons are driving towards each other, their relative speed is the sum of their individual speeds.
Relative Speed=12+14=26 km/h
Determine Distance to be Covered
The initial distance between them is 56 km. We need to find the time when they are 4 km apart, meaning the total distance they must cover together is:
Deffective=56−4=52 km
Calculate Time
Using the formula for time taken with relative speed, we divide the effective distance by the relative speed:
t=2652=2 hours
D is correct because the effective distance to be covered by both persons together is 56−4=52 km at a relative speed of 12+14=26 km/h, resulting in a time of 2 hours.
Problems involving objects moving towards or away from each another can always be simplified by transforming them into a single moving object using relative speed.
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