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Two cities, A and B, are connected by means of a highway 150 kms long. An automobile leaves A at
1:00 pm and travels at a uniform rate of 40 kms per hour toward B. Thirty minutes later, another
automobile leaves city A and travels toward B at a uniform rate 55 kms per hour. At what time will
the second car overtake the first car?
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Let t be the time after 1:00 pm, in hours.
The distance traveled by first auto is 40t kilometers.
The distance traveled by the second auto is 55*(t-0.5) kilometers.
We want to find t when the distance is the same (overtake condition)
40t = 55(t-0.5).
Simplify this equation and find t
40t = 55t - 0.5*55
0.5*55 = 55t - 40t
27.5 = 15t
t = 27.5/15 = 55/30 = 110/60 = 1 hour and 50 minutes.
The second auto will overtake the first at 1 hour and 50 minutes after 1:00 pm, which is 2:50 pm.
The traveled distance is less than 40 km/h * 2 hours = 80 kilometers;
hence, the second car overtakes the first one before than either car will get the city B.
Solved.
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- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
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