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Problems based on Time Distance and Speed
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In solving problems based on time, distance and speed we use the following formulae:
Distance = Speed * Time
Time = Distance / Speed
and Speed = Distance / time
Also, if
Speed of a boat in still water = u km/hr
Speed of the current = v km/hr,
Speed upstream = (u - v) km/hr
Speed down stream = (u + v) km/hr
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Example: Two trains, traveling towards each other, left from two stations that are 820 miles apart, at 4 pm. If the rate of the first train is 80 mph and the rate of the second train is 84 mph, at what time will they pass each other?
Solution:-After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by
  D1 = 80 t and D2 = 84 t
After t hours total distance D traveled by the two trains is given by
D = D1 + D2 = 80 t + 84 t = 164 t
When distance D is equal to 900 miles, the two trains pass each other.
164t = 820
Solve the above equation for t
= 5 hours.
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