A car travels at a speed of 50km/h for 30min , at 30km/h for the next 15min and then
at 70km/h for next 45min what is the average speed of car?
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Oh I'm Suhani from WB class 11 ^•^
Answers
Explanation:
Given :
First case :-
Speed of the car = 50 km/hr
Time = 30 minutes
Second case :-
Speed of the car = 30 km/hr
Time = 15 minutes
Third case :-
Speed of the car = 70 km/hr
Time = 45 minutes
To find :
Average speed of the car
Concept :
Firstly, calculate the distance travelled by the car in each case. Then after getting the value of distance in all the cases use the formula to calculate the average speed. The resultant value will our required answer.
Distance is the path travelled by an object.
Mathematically,
Formula to calculate distance :-
Distance = Speed × Time
Average speed is the total distance travelled by a body divided by the total time taken.
Mathematically,
Formula to calculate average speed :-
Average speed = Total distance travelled ÷ Total time taken
Solution :
First case →
Firstly, convert the time from minutes in hours.
As we know,
1 minute = 1/60 hr
Divide the value by 69 to convert it from minutes into hours.
→ Time = 30/60
→ Time = 3/6
→ Time = 1/2
• Time = 1/2 hrs
Distance travelled by the car in the first case :-
➪ Distance = Speed × Time
Substituting the given values,
➪ Distance = 50 × 1/2
➪ Distance = 25
Distance travelled by the car in first 30 minutes = 25 km
Second case →
Time = 15 minutes
• 1 min = 1/60 hr
→ Time = 15/60
→ Time = 5/20
• Time = 5/20 hrs
Distance travelled by the car in the second case :-
➪ Distance = Speed × Time
Substituting the given values,
➪ Distance = 30 × 5/20
➪ Distance = 3 × 5/2
➪ Distance = 15/2
➪ Distance = 7.5
Distance travelled by the car in next 15 minutes = 7.5 km
Third case →
→ Time = 45 minutes
→ Time = 45/60
→ Time = 9/12
→ Time = 3/4
• Time = 3/4 hrs
Distance travelled by the car in the third case :-
➪ Distance = Speed × Time
Substituting the given values,
➪ Distance = 70 × 3/4
➪ Distance = 35 × 3/2
➪ Distance = 105/2
➪ Distance = 52.5
Distance travelled by the car in next 45 minutes = 52.5 km
Now, calculating the average speed :-
Average speed = Total distance travelled ÷ Total time taken
→ Total distance travelled = 25 + 7.5 + 52.5
→ Total distance travelled = 85
Total distance travelled by the car = 85 km
→ Total time taken = 1/2 + 5/20 + 3/4
→ Total time taken = 1/2 + 1/4 + 3/4
→ Total time taken = (2 + 1 + 3)/4
→ Total time taken = 6/4
→ Total time taken = 3/2 = 1.5
Total time taken = 1.5 hrs
We have,
Total distance = 85 km
Total time = 1.5 hrs
Substitute the values in the formula of average speed :-
➪ Average speed = 85/1.5
➪ Average speed = 56.67
Therefore,
The average speed of car = 56.67 km/hr
Explanation:
Answer in the figure
Hope this will help you
