A boat goes 24 , km upstream and 28 , km down | vedclass

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

Question

(D) Let the speed of the boat in still water be $x \, km/hr$ and the speed of the stream be $y \, km/hr$.Upstream speed $= (x - y) \, km/hr$ and downs

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let the speed of the boat in still water be $x \, km/hr$ and the speed of the stream be $y \, km/hr$.Upstream speed $= (x - y) \, km/hr$ and downstream speed $= (x + y) \, km/hr$.According to the problem:$1) \frac{24}{x-y} + \frac{28}{x+y} = 6$$2) \frac{30}{x-y} + \frac{21}{x+y} = 6.5 = \frac{13}{2}$Let $u = \frac{1}{x-y}$ and $v = \frac{1}{x+y}$.$24u + 28v = 6 \implies 12u + 14v = 3$ (Equation $i$)$30u + 21v = \frac{13}{2} \implies 60u + 42v = 13$ (Equation $ii$)Multiply equation $i$ by $3$: $36u + 42v = 9$ (Equation $iii$)Subtract equation $iii$ from $ii$: $(60u - 36u) = 13 - 9 \implies 24u = 4 \implies u = \frac{1}{6}$.Substitute $u = \frac{1}{6}$ in equation $i$: $12(\frac{1}{6}) + 14v = 3 \implies 2 + 14v = 3 \implies 14v = 1 \implies v = \frac{1}{14}$.So,$x - y = 6$ and $x + y = 14$.Adding the two equations: $2x = 20 \implies x = 10 \, km/hr$.

$A$ boat goes $24 \, km$ upstream and $28 \, km$ downstream in $6 \, hours$. It goes $30 \, km$ upstream and $21 \, km$ downstream in $6 \, hours$ and $30 \, minutes$. The speed of the boat in still water is $...... \, km/hr$.

Similar Questions

$A$ boat moves downstream at the rate of $1 \, km$ in $10 \, minutes$ and upstream at the rate of $4 \, km/h$. What is the velocity of the current (in $km/h$)?

$A$ man can row at $5 \text{ km/hr}$ in still water. If the velocity of the current is $1 \text{ km/hr}$ and it takes him $1 \text{ hour}$ to row to a place and come back,how far is the place? (in $\text{km}$)

Speeds of a boat along the current and against the current are $10 \ km/hr$ and $8 \ km/hr$ respectively. What is the speed (in $km/hr$) of the current?

What time will be taken by a boat to cover a distance of $128\, km$ along the stream,if the speed of a boat in still water is $24\, km/h$ and the speed of the stream is $8\, km/h$? (in $h$)

The current of a stream runs at $1 \, km/h$. $A$ motor boat goes $35 \, km$ upstream and back again to the starting point in $12 \, hours$. The speed of the motor boat in still water in $km/h$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module