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A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in first hour was 30 km, is
- a)266 km
- b)273 km
- c)280 km
- d)287 km
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A car driver increases the average speed of his car by 3 km/hr every h...
Distance travelled in 1st hour = 30 km
So initial speed = D/T = 30/1 = 30 km/hr
Now, Speed in 2nd hour = 33 km/hr
So distance covered in 2nd hour = 33 x 1 = 33 km
Similarly distance covered in 3rd, 4th, 5th, 6th and 7th hours will be 36, 39, 42, 45 and 48 km.
i.e. distance travelled each hour is an AP with first term as 30 and common difference of 3.
So Total Distance = Sum of 7 terms = 7/2 x (60 + 6 x 3) = 7/2 x 78 = 7 x 39 = 273 km
So initial speed = D/T = 30/1 = 30 km/hr
Now, Speed in 2nd hour = 33 km/hr
So distance covered in 2nd hour = 33 x 1 = 33 km
Similarly distance covered in 3rd, 4th, 5th, 6th and 7th hours will be 36, 39, 42, 45 and 48 km.
i.e. distance travelled each hour is an AP with first term as 30 and common difference of 3.
So Total Distance = Sum of 7 terms = 7/2 x (60 + 6 x 3) = 7/2 x 78 = 7 x 39 = 273 km
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Community Answer
A car driver increases the average speed of his car by 3 km/hr every h...
To solve this problem, we can use the concept of arithmetic progression (AP).
The average speed of the car is increasing by 3 km/hr every hour. This means that the speed of the car at the end of each hour is 3 km/hr more than the speed at the beginning of that hour.
Let's break down the problem step by step:
1. Speed at the end of the first hour: The speed at the beginning of the first hour is given as 30 km/hr. Since the speed increases by 3 km/hr every hour, the speed at the end of the first hour will be 30 + 3 = 33 km/hr.
2. Speed at the end of the second hour: The speed at the end of the first hour was 33 km/hr. Since the speed increases by 3 km/hr every hour, the speed at the end of the second hour will be 33 + 3 = 36 km/hr.
3. Similarly, we can calculate the speed at the end of each subsequent hour:
- Speed at the end of the third hour: 36 + 3 = 39 km/hr
- Speed at the end of the fourth hour: 39 + 3 = 42 km/hr
- Speed at the end of the fifth hour: 42 + 3 = 45 km/hr
- Speed at the end of the sixth hour: 45 + 3 = 48 km/hr
- Speed at the end of the seventh hour: 48 + 3 = 51 km/hr
Now, we need to calculate the total distance traveled in 7 hours. To do this, we can calculate the sum of the distances traveled at the end of each hour.
Using the formula for the sum of an AP, which is given by Sn = n/2(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term, we can calculate the total distance traveled.
Let's calculate the sum:
- Number of terms (n) = 7
- First term (a) = 30 km/hr
- Last term (l) = 51 km/hr
Using the formula, Sn = 7/2(30 + 51), we get:
Sn = 7/2(81)
Sn = 7/2 * 81
Sn = 7 * 40.5
Sn = 283.5 km
Therefore, the total distance traveled in 7 hours is 283.5 km, which is closest to option (b) 273 km.
The average speed of the car is increasing by 3 km/hr every hour. This means that the speed of the car at the end of each hour is 3 km/hr more than the speed at the beginning of that hour.
Let's break down the problem step by step:
1. Speed at the end of the first hour: The speed at the beginning of the first hour is given as 30 km/hr. Since the speed increases by 3 km/hr every hour, the speed at the end of the first hour will be 30 + 3 = 33 km/hr.
2. Speed at the end of the second hour: The speed at the end of the first hour was 33 km/hr. Since the speed increases by 3 km/hr every hour, the speed at the end of the second hour will be 33 + 3 = 36 km/hr.
3. Similarly, we can calculate the speed at the end of each subsequent hour:
- Speed at the end of the third hour: 36 + 3 = 39 km/hr
- Speed at the end of the fourth hour: 39 + 3 = 42 km/hr
- Speed at the end of the fifth hour: 42 + 3 = 45 km/hr
- Speed at the end of the sixth hour: 45 + 3 = 48 km/hr
- Speed at the end of the seventh hour: 48 + 3 = 51 km/hr
Now, we need to calculate the total distance traveled in 7 hours. To do this, we can calculate the sum of the distances traveled at the end of each hour.
Using the formula for the sum of an AP, which is given by Sn = n/2(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term, we can calculate the total distance traveled.
Let's calculate the sum:
- Number of terms (n) = 7
- First term (a) = 30 km/hr
- Last term (l) = 51 km/hr
Using the formula, Sn = 7/2(30 + 51), we get:
Sn = 7/2(81)
Sn = 7/2 * 81
Sn = 7 * 40.5
Sn = 283.5 km
Therefore, the total distance traveled in 7 hours is 283.5 km, which is closest to option (b) 273 km.
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A car driver increases the average speed of his car by 3 km/hr every hour. The total distance travelled in 7 hours if the distance covered in first hour was 30 km, isa)266 kmb)273 kmc)280 kmd)287 kmCorrect answer is option 'B'. Can you explain this answer?
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