Question

A train travels with a speed of 60 km/hr in 0.52 hrs, 30 km/hr in 0.24 hrs.  Then 70km/hr in 0.71 hr.  calculate the average speed of he train

Answer 1

Answer:

Explanation:

Given :-

First speed, v₁ = 60 km/h

Time taken for this part of trip, t₁ = 0.52 h

Second speed, v₂ = 30 km/h

Time taken for this part of trip, t₂ = 0.24 h

Third speed, v₃ = 70 km/h

Time taken for this part of trip, t₃ = 0.71 h

To Calculate :-

Average speed, V(avg) = ???

Formula to be used :-

Distance = Speed × Time

V(avg) = Total distance/Total time taken

Solution :-

Now, in this case we are not given the total distance traveled. so first of all we will find out the distance covered during the three given intervals by using the formula,

Distance = Speed × Time

(i) 1st part, d₁ = v₁ × t₁ = 60 × 0.52 = 156/5 km

(ii) 2nd part, d₂ = v₂ × t₂ = 30 × 0.24 = 36/5 km

(iii) 3rd part, d₃ = v₃ × t₃ = 70 × 0.71 = 497/10 km

Total distance, d = d₁ + d₂ + d₃

= 156/5 + 36/5 + 497/10 = 881/10 = 88.1 km

Total time taken, t = t₁ + t₂ + t₃

= 0.52 + 0.24 + 0.71 = 1.47 h

Now,

V(avg) = Total distance/Total time taken

⇒ V(avg) = 88.1/1.47

⇒ V(avg) = 59.93 km/h.

Hence, the average speed of the train is 59.93 km/h.

Answer 2

Answer:

Given:A train travels at a speed of 60km/h for 0.52h, of 30km/h for the next 0.24h, and then at 70km/h for the next 0.71h.

We need to find the average speed of the train.

Let us consider the first case,

The train travels at a speed of 60 km/h for a time of 0.52 h

We know that Speed = distance / time = 30km/hr

Hence Distance = Speed X Time

Distance=60 x 0.52 = 31.2 km ————–(i)

Now, in the second case, the train travels at a speed of 30 km/h for a time of 0.24 hr.

We know that speed = distance / time = 30 km/hr

Distance = Speed X Time

Distance=30 × 0.24 = 7.2 km ———–(ii)

Here in the third case, the train travels at a speed of 70km/h for a time of 0.71 hr.

We know thatspeed = distance / time = 70km/hr

Hence Distance = Speed X Time

=70 × 0.71 hr .

speed = distance / time = 70km/hr

Distance = 70 × 0.71 = 49.7 km ———–(iii)

Combining all the equations (i), (ii) and (iii) and adding we get,

Total distance travelled

= (31.2 + 7.2 + 49.7) km = 88.1 km .

Total time taken = (0.52 + 0.24 + 0.71) hr = 1.47 hr .

Average speed = Total distance travelled / Total time taken

= (88.1/1.47) km /hr

Hence, average speed = 59.9 km/hr

Explanation:

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