The relationships between distance, speed and time :
Time = Distance / Speed
Speed = Distance / Time
Distance = Time ⋅ Speed
Let us look at some examples to understand how to solve word problems involving speed.
Example 1 :
A passenger train takes 3 hours less than a slow train for journey of 600 km. If the speed of the slow train is 10 km/hr less than that of the passenger train, find the speed of two trains.
Here speed of slow train is compared with speed of passenger train.
Let x be the speed of the of the passenger train.
Speed of the slow train is 10 km/hr less than that of the passenger train.
So, x - 10 be the speed of the slow train.
Distance has to be covered = 600 km
Time = Distance/speed
Let t1 and t2 be the time taken by passenger train and slow train respectively.
The differences of time taken by both trains are 3 hours
t1 = 600 / x
t2 = 600 / (x - 10)
t1 - t2 = 3 hours
[600 / (x – 10)] – [600 / x] = 3
600[ (1/(x - 10) - (1/x)] = 3
200 [ x - (x - 10) / x(x - 10) ] = 1
200 [10/x2 – 10x] = 1
2000 = x2 – 10x
x2 – 10x - 2000 = 0
(x + 40) (x – 50) = 0
x + 40 = 0
x = -40
x - 50 = 0
x = 50
Therefore the speed of passenger train = 50 km/hr
Speed of slow train = 40 m/hr
Example 2 :
Mr John traveled by scooter from his house to a town that was some distance away. If he traveled at a constant speed of 50 km/hr, he would have arrived at 11 am. If he traveled at 75 km/hr, he would have arrived at 10 am. At what speed should be riding he wanted to arrive at 10.30 am ?
If he travels the distance at the speed of 50 km/hr, he can reach the spot at 11 am.
If he travels the distance at the speed of 75 km/hr, then he will reach the spot at 10 am. The difference between two timings is 1 hour.
Bu we do not know at what time he started his travelling.
Time = Distance / Speed
Time = Distance / 50 -----(1)
Time = Distance / 75 -----(2)
(1) - (2)
1 = (D / 50) - (D / 75)
1 = (3D - 2D)/150
D = 150
150 km is the required distance. By applying the value of D in (1), we get
Time = 150/50
Time = 3 hours
He is taking 3 hours to cover the distance 150 km. So, he started his travelling at 8 am. But he should cover the distance with in 2 1/2 hours.
2 1/2 = 150 / Speed
5/2 = 150 / Speed
Speed = 150 (2/5)
Speed = 60 km/hr
The required speed is 60 km/hr.
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