Question

A motorist travels to a place 150 km away at and average speed of 50km/hour and returns at 30km/hour. What is the average speed for the whole journey

Answer 1

the average speed for the whole journey is 37.5

Answer 2

Answer:

Avg. Speed for the whole Journey = 37.5 km/h

Step-by-step explanation:

We can solve it in two ways

Method 1 (Long process)

We know that,

Avg. Speed

= Total Distance covered/Total Time taken

Now,

Total Distance = 150 km + 150 km

Because he went to the destination and came back to the same point.

Total Distance = 300 km

Now, we know that,

Speed = Distance/Time

Then,

Time = Distance/Speed

Now,

Time taken from point A to destination = 150/50

T1 = 3 hrs

Time taken from destination to point A = 150/30

T2 = 5 hrs

Total Time taken = T1 + T2

= 3 + 5

= 8 hrs

So,

Avg. Speed

= Total Distance covered/Total Time taken

Avg. Speed = 300/8

= 150/4

= 75/2

= 37.5 km/h

Hence,

Avg. Speed for the whole Journey = 37.5 km/h

Method 2 (Easy substitution)

We should know that,

Avg. Speed = 2(S1)(S2)/[S1 + S2]

Here, let's just prove it and see what we get, it definitely easier this way

So,

Let the distance from point A to destination be D

Then,

Total Distance = Distance from point A to destination + Destination to Point A

Total Distance = D + D = 2D

Now,

Let the Average speed taken during the journey be S1 from point A to destination and S2 from destination to point A.

So,

S1 = D/T1

then,

T1 = D/S1

Similarly,

S2 = D/T2

T2 = D/S2

Now,

Total time = T1 + T2

= (D/S1) + (D/S2)

Taking D common,

= D[(1/S1) + (1/S2)]

= D[(S1 + S2)/(S1 × S2)]

= D(S1 + S2)/(S1S2)

Now,

Avg. Speed = Total Distance/Total time

Avg. Speed = 2D/[D(S1 + S2)/(S1S2)]

Cancelling common factor D

Avg. Speed = 2/[S1 + S2)/(S1S2)]

Avg. Speed = 2 ÷ (S1 + S2)/(S1S2)

Avg. Speed = 2 × (S1S2)/(S1 + S2)

∴ Avg. Speed = 2(S1)(S2)/(S1 + S2)

So, here,

S1 = 50 km/h

S2 = 30 km/h

So,

Avg. Speed = (2 × 50 × 30)/(50 + 30)

Avg. Speed = (3000/80)

Avg. Speed = 300/8

Avg. Speed = 37.5 km/h

Hence,

Avg. Speed for the whole Journey = 37.5 km/h

Hope it helped you and believing you understood it...All the best