
A train travels at $60 km/h$ for $0.52h$, at $30 km/h$ for the next $0.24h$ and at $70 km/h$ for the next $0.71h$. What is the average speed of the train?
A. $125km/h$
B. $10 km/h$
C. $20 km/h$
D. $59.9 km/h$
Answer
464.7k+ views
Hint:The average speed of the train is given by the total distance travelled by train divided by the total time taken by it to travel that distance. We have to find the distance travelled in various time periods and then calculate the average speed by the before mentioned formula.
Complete step by step answer:
Average speed is actually the speed that an object needs to travel at so as to cover the same total distance in the same time that it did at different speeds for different time periods.
We have to calculate the total distance travelled by train in various time periods.
In the first case, the train travels at a speed of 60 km/h for 0.52hr
Now, speed = distance/time=60km/h
Distance= $60 \times 0.52 = 31.2km$
In the second case, the train travels at a speed of 30km/h for 0.24hr
Distance= $30 \times 0.24 = 7.2km$
In the third case, the train travels at a speed of 70km/h for a time of 0.71 hr, so
Distance= $70 \times 0.71 = 49.7km$
Now, we get the total distance travelled as,
$\Rightarrow 31.2 + 7.2 + 49.7 = 88.1km$
Also, we can get the total of travel as
$\Rightarrow0.52 + 0.24 + 0.71 = 1.47hr$
So, the average speed can be calculated now as,
Average speed = Total distance travelled / Total time taken
$\therefore v = \dfrac{{88.1km}}{{1.47hr}} = 59.9km/hr$
Therefore, the correct answer is option D.
Note:The units can also be converted to m/s and solved, that is however the options demand. Here, because all the options are in km/h , we needn’t convert the units. Also, we have to note that the average speed isn’t simply the average of all speeds, which is a common mistake made by students.
Complete step by step answer:
Average speed is actually the speed that an object needs to travel at so as to cover the same total distance in the same time that it did at different speeds for different time periods.
We have to calculate the total distance travelled by train in various time periods.
In the first case, the train travels at a speed of 60 km/h for 0.52hr
Now, speed = distance/time=60km/h
Distance= $60 \times 0.52 = 31.2km$
In the second case, the train travels at a speed of 30km/h for 0.24hr
Distance= $30 \times 0.24 = 7.2km$
In the third case, the train travels at a speed of 70km/h for a time of 0.71 hr, so
Distance= $70 \times 0.71 = 49.7km$
Now, we get the total distance travelled as,
$\Rightarrow 31.2 + 7.2 + 49.7 = 88.1km$
Also, we can get the total of travel as
$\Rightarrow0.52 + 0.24 + 0.71 = 1.47hr$
So, the average speed can be calculated now as,
Average speed = Total distance travelled / Total time taken
$\therefore v = \dfrac{{88.1km}}{{1.47hr}} = 59.9km/hr$
Therefore, the correct answer is option D.
Note:The units can also be converted to m/s and solved, that is however the options demand. Here, because all the options are in km/h , we needn’t convert the units. Also, we have to note that the average speed isn’t simply the average of all speeds, which is a common mistake made by students.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
