HOW TO SOLVE WORD PROBLEMS INVOLVING SPEED

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.

Solution :

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

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 ?

Solution :

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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