If a distance of 50, m is covered in 1, minut | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The distances covered in consecutive minutes are as follows:Distance in $1^{st}$ minute $= 50\, m$.Distance in $2^{nd}$ minute $= 90 - 50 = 40\, m

Vedclass · Accepted Answer

$610$

Vedclass · Answer

(A) The distances covered in consecutive minutes are as follows:Distance in $1^{st}$ minute $= 50\, m$.Distance in $2^{nd}$ minute $= 90 - 50 = 40\, m$.Distance in $3^{rd}$ minute $= 130 - 90 = 40\, m$.Since the distance covered in each subsequent minute is constant $(40\, m)$,this forms an arithmetic progression where the first term $a = 50$ and the common difference $d = 40$.The total distance covered in $n$ minutes is given by the sum of the first $n$ terms of an arithmetic progression: $S_n = \frac{n}{2} [2a + (n - 1)d]$.For $n = 15$:$S_{15} = \frac{15}{2} [2(50) + (15 - 1)40]$$S_{15} = \frac{15}{2} [100 + 14 	imes 40]$$S_{15} = \frac{15}{2} [100 + 560]$$S_{15} = \frac{15}{2} 	imes 660 = 15 	imes 330 = 4950\, m$.Wait,re-evaluating the question: The values $50, 90, 130$ represent the *total* distance covered up to that time. Thus,the sequence is $50, 90, 130, \dots$ which is an arithmetic progression with $a = 50$ and $d = 40$.The distance at $n = 15$ is the $15^{th}$ term: $a_{15} = a + (n - 1)d$.$a_{15} = 50 + (15 - 1)40 = 50 + 14 	imes 40 = 50 + 560 = 610\, m$.

If a distance of $50\, m$ is covered in $1\, minute$,$90\, m$ in $2\, minutes$,and $130\, m$ in $3\, minutes$,find the total distance covered in $15\, minutes$ (in $m$).

Similar Questions

How many seconds will a $500 \, m$ long train take to cross a man walking with a speed of $3 \, km/h$ in the direction of the moving train, if the speed of the train is $63 \, km/h$?

$A$ train running at the speed of $84 \, km/h$ passes a man walking in the opposite direction at the speed of $6 \, km/h$ in $4 \, s$. What is the length of the train (in $meters$)?

The ratio between the speed of a bike and a train is $15:27$ respectively. Also,a bus covers a distance of $720 \, km$ in $9 \, hours$. The speed of the bike is three-fourths the speed of the bus. How much distance will the train cover in $7 \, hours$? (in $km$)

$A$ person travels from $P$ to $Q$ at a speed of $40 \, km/hr$ and returns by increasing his speed by $50 \%$. What is his average speed for both the trips? (in $km/hr$)

If $I$ walk at $5\, km/hr$,$I$ miss a train by $7\, minutes$. However,if $I$ walk at $6\, km/hr$,$I$ reach the station $5\, minutes$ before the departure of the train. The distance between my house and the station is (in $km$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module