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

$A$ man travelled from the village to the post office at the rate of $25 \, km/hr$ and walked back at the rate of $4 \, km/hr$. If the whole journey took $5 \, hours \, 48 \, minutes$,find the distance of the post office from the village (in $km$).

$A$ train is running at a uniform speed of $60 \, km/h$. It passes a railway platform in $15 \, s$. If the length of the platform is $130 \, m$,then the length of the train is (in $m$):

$A$ boy rides his bicycle $10 \, km$ at an average speed of $12 \, km/hr$ and again travels $12 \, km$ at an average speed of $10 \, km/hr$. His average speed for the entire trip is approximately (in $km/hr$)

$A$ car travels the first $39 \, km$ distance in $45 \, minutes$ and the next $25 \, km$ distance in $35 \, minutes$. What is its average speed in $km/h$?

$A$ train $700 \, m$ long is running at a speed of $72 \, km/hr$. If it crosses a tunnel in $1 \, minute$,then the length of the tunnel (in $metres$) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module