Application of equation in solving problem is related to our day - to - day life. There is a wide variety of such problems which are generally called " word problems ". In solving problems based on time , distance and speed, we use the following formulae given below:
Distance – Rate (or speed ) – Time
The equation which relates distance , rate (or speed ) and time is given by
Distance = Rate * Time
The equation which relates distance, rate, and time is
D = R . T
where D is the distance travelled, R is the rate, and T is the time.
Or,
Distance = Speed × Time
Time = Distance / Speed
Speed = Distance / Time
Points to Remember
- If two trains are moving in the same direction, their relative velocity(i.e, speed) is equal to the difference of speed.
- If they are moving in opposite directions, then their relative speed is equal to the sum of their speed.
- A speed of 90 kilometres per hour = 25 metres per second.
Problems Based on Distance – Rate (or Speed) – Time
EXAMPLE A Train 200 metres long takes 20 seconds to cross a platform 300 metres long. The speed of the train in metres per second is :
SOLUTION For crossing the platform, the train has to pass its own length of 200 metres as well as the length of the platform 300 metres.
Total distance passed = 200 + 300
= 500 metres
Time taken = 20 seconds
Hence the speed of train = 25 m/sec
EXAMPLE A passenger train 140 metres long travelling at a speed of 80km crosses a train 185 metres long coming from the opposite direction in 8 seconds. What is the speed of the second train?
SOLUTION Lengths of two trains = 140 + 185
= 325 m
= 325 / 1000 km
Let the speed of 2nd train = x km/hr
Now speed of first train = 80 km/hr
Therefore, Relative speed of the trains = (80 + x) km/hr
Distance travelled in 8 sec = [(80 + x) / (60 × 60 )] × 8
= 325 / 1000 km
On solving x = 66.25 km/hr
EXAMPLE The distance between two cities is 500 km. A car starts from the first town with a speed of 30km/hour. At the same time another car starts from the second town with a speed of 50 km per hour. What is the distance of the point where they meet from the first town?
SOLUTION Let the two cars meet at a distance x km from first town.
x / 30 = ( 500 - x ) / 50
50 x = 15000 - 30 x
80 x = 15000
Or, x = 15000 / 80
= 187.5 km
Related Tags
Problems for Rates, Average Speed, Distance, And Time, Problems: Rates, Average Speed, Distance, And Time, Problems (Rates, Average Speed, Distance, And Time)