A horse rider travels on horseback from Bhopa | vedclass

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

Question

(A) Let the distance be $d \, km$ and the initial speed be $s \, km/h$.From the first condition: $\frac{d}{s} - \frac{d}{s+6} = 4 \implies \frac{6d}{s

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(A) Let the distance be $d \, km$ and the initial speed be $s \, km/h$.From the first condition: $\frac{d}{s} - \frac{d}{s+6} = 4 \implies \frac{6d}{s(s+6)} = 4 \implies \frac{d}{s(s+6)} = \frac{2}{3} \implies d = \frac{2s(s+6)}{3} \dots (i)$From the second condition: $\frac{d}{s-6} - \frac{d}{s+6} = 10 \implies d \left( \frac{(s+6) - (s-6)}{(s-6)(s+6)} ight) = 10 \implies d \left( \frac{12}{s^2-36} ight) = 10 \implies d = \frac{10(s^2-36)}{12} = \frac{5(s^2-36)}{6} \dots (ii)$Equating $(i)$ and $(ii)$: $\frac{2s^2+12s}{3} = \frac{5s^2-180}{6} \implies 4s^2 + 24s = 5s^2 - 180 \implies s^2 - 24s - 180 = 0$.Solving the quadratic equation: $(s-30)(s+6) = 0$. Since speed cannot be negative,$s = 30 \, km/h$.Substituting $s = 30$ into $(i)$: $d = \frac{2(30)(36)}{3} = 20 	imes 36 = 720 \, km$.

Similar Questions

$A$ hare sees a dog $100\, m$ away from her and runs off in the opposite direction at a speed of $12\, km/h$. $A$ minute later,the dog perceives her and gives chase at a speed of $16\, km/h$. How much distance is covered by the hare after being spotted? (in $m$)

Car $A$ runs at the speed of $65 \text{ km/h}$ and reaches its destination in $8 \text{ hours}$. Car $B$ runs at the speed of $70 \text{ km/h}$ and reaches its destination in $4 \text{ hours}$. What is the respective ratio of distances covered by Car $A$ and Car $B$?

$A$ man can reach a certain place in $30 \, \text{hours}$. If he reduces his speed by $\frac{1}{15}^{th}$, he goes $10 \, \text{km}$ less in that same time. Find his speed in $\text{km/hr}$.

If a boy travels from his house to school at the rate of $4 \, km/h$,he reaches the school $10 \, minutes$ earlier than the scheduled time. However,if he walks at the rate of $3 \, km/h$,he reaches $10 \, minutes$ late. Find the distance of the school from his house (in $km$).

Ravi and Ajay start simultaneously from a place $A$ towards $B$,$60 \, km$ apart. Ravi's speed is $4 \, km/h$ less than that of Ajay. Ajay,after reaching $B$,turns back and meets Ravi at a place $12 \, km$ away from $B$. Ravi's speed is (in $km/h$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module