The average speed of a train in the onward jo | vedclass

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

Question

(C) Let the speed of the return journey be $v_r = x\, 	ext{km/h}$.Then,the speed of the onward journey is $v_o = x - 0.25x = 0.75x = \frac{3}{4}x\, \

Vedclass · Accepted Answer

$43.75$

Vedclass · Answer

(C) Let the speed of the return journey be $v_r = x\, 	ext{km/h}$.Then,the speed of the onward journey is $v_o = x - 0.25x = 0.75x = \frac{3}{4}x\, 	ext{km/h}$.The total distance for the to and fro journey is $800 + 800 = 1600\, 	ext{km}$.The total time spent is $17\, 	ext{hours}$,including a $1\, 	ext{hour}$ halt. Thus,the actual travel time is $17 - 1 = 16\, 	ext{hours}$.Time taken for onward journey $t_o = \frac{800}{v_o} = \frac{800}{3x/4} = \frac{3200}{3x}$.Time taken for return journey $t_r = \frac{800}{v_r} = \frac{800}{x}$.Total travel time $t_o + t_r = 16\, 	ext{hours}$.$\frac{3200}{3x} + \frac{800}{x} = 16$.Multiply by $3x$: $3200 + 2400 = 48x$.$5600 = 48x \implies x = \frac{5600}{48} = \frac{350}{3} \approx 116.67\, 	ext{km/h}$.Speed of the onward journey $v_o = \frac{3}{4}x = \frac{3}{4} 	imes \frac{350}{3} = \frac{350}{4} = 87.5\, 	ext{km/h}$.Wait,re-evaluating the problem statement: If the total distance covered is $800\, 	ext{km}$ for the whole trip (i.e.,$400\, 	ext{km}$ one way):$t_o + t_r = 16 \implies \frac{400}{3x/4} + \frac{400}{x} = 16 \implies \frac{1600}{3x} + \frac{1200}{3x} = 16 \implies \frac{2800}{3x} = 16 \implies 48x = 2800 \implies x = 58.33$.$v_o = \frac{3}{4} 	imes 58.33 = 43.75\, 	ext{km/h}$.Thus,the speed of the onward journey is $43.75\, 	ext{km/h}$.

Similar Questions

The average height of the students of a class of $20$ is $105 \, cm$. If ten more students of average height of $120 \, cm$ join this class,the average height of the class will become (in $cm$)?

The average of $20$ numbers is $30$ and that of other $30$ numbers is $50$. What is the average of all the numbers?

The average weight of $A, B$ and $C$ is $45\, kg$. If the average weight of $A$ and $B$ is $40\, kg$ and that of $B$ and $C$ is $43\, kg$,then the weight of $B$ is (in $, kg$)

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2},$ then the average of $(m + n)$ numbers is

The average salary of $15$ persons is $Rs. 5,500$. If the salary of one person is added,the average increases to $Rs. 5,700$. What is the salary of this one person in $Rs.$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module