Question

A train travels along a straight line at a constant speed of 60 mph for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mph what is the average speed of the train for the whole journey​

Answer 1

Answer:

72 mph

Step-by-step explanation:

Case I:

Speed of the train = 60 mph

Distance travelled = d

Therefore, we have,

=> Time taken, t1 = d/60

Case II:

Speed of the train = 80 mph

Distance travelled = 2d

Therefore, we have,

=> Time taken, t2 = 2d/80

=> t2 = d/40

Now, to find the average speed of the train.

We know that,

Avg. Speed, v = Total distance/Total time

Here, we have,

=> Total distance = d + 2d = 3d

=> Total time = t1+t2 = d/60 + d/40

Substituting the values,

Therefore, we will get,

=> v = 3d/(d/60 + d/40)

=> v = 3d/{(40d+60d)/(40×60)}

=> v = 3d/(100d/2400)

=> v = 2400 × 3d/100d

=> v = 2400 × 3/100

=> v = 24 × 3

=> v = 72

Hence, the average speed is 72 mph.

Answer 2

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We know that,

Average speed = Total distance/Total time

Speed = v₁ = 60 mph

Distance travelled = S₁ = d

Time taken = S₁ / v₁ = d/60

Speed = v₂ = 80 mph

Distance travelled = S₂ = 2d

Time taken = S₂ / v₂ = 2d/80 = d/40

Therefore,

Total distance = d + 2d = 3d

Total time = d/60 + d/40

                 = (4d + 6d)/240

                 = 10d/240

                 = d/24

Average velocity = Total DIstance / Total Time

                              = (3d) / (d/24)

                              = 3*24

                              = 72 mph

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