Question

a Boat covers 32 km upstream and 36 km downstream in 7 hours. it covers 40 km upstream and 48 kilometre downstream in 9 hours .
class 10 RD Sharma ​

Answer 1

$\huge \fbox{\sf{\underline{answer}}} \rightarrow$

$\sf \green{ \underline{given : }}$

• A Boat covers 32 km upstream and 36 km downstream in 7 hours

$\sf \green{ \underline{solution : }}$

$\sf{let \: the \: speed \: of \: boat \:in \: still \: water \: = x.}$

$\sf {speed \: of \: stream = y}$

$\sf{ \underline{ \bigstar \: first \: condition}}$

$\sf{1) \: speed \: of \: the \: boat \: in \: downstream \: = (x + y)}$

$\sf{distance \: travelled = d1 = 36}$

$\sf \red{speed = \frac{distance}{time} }$

$\sf{ \therefore \: t1(time) \: = \frac{36}{(x + y)} }$

$\sf{ 2) \: speed \: of \: boat \: in \: upstream = (x - y)}$

$\sf{distance \: travelled = d2 = 32}$

$\sf \red{speed = \frac{distance}{time} }$

$\sf{t2(time) = \frac{32}{x - y} }$

$\sf{total \: time = 7 \: hours}$

$\sf{ \therefore \: t1 + t2 = 7}$

$\sf{ \therefore \: \frac{36}{(x + y)} + \frac{32}{(x - y)}...(1)}$

$\sf{ \underline{ \bigstar \: second \: condition}}$

$\sf{1) \: speed \: of \: boat \: in \: downstream \: = (x + y)}$

$\sf{distance \: travelled = d2 = 48}$

$\sf \red{speed = \frac{distance}{time} }$

$\sf{ \therefore \: t3(time) = \frac{48}{(x + y)} }$

$\sf{2) \: speed \: of \: the \: boat \: in \: upstream = (x - y)}$

$\sf{distance \: travelled = d4 = 40}$

$\sf \red{speed = \frac{distance}{time} }$

$\sf{t4(time) = \frac{40}{(x - y)} }$

$\sf{total \: time = 9 \: hour}$

$\sf{ \therefore \: t3 + t4 = 9}$

$\sf{ \therefore \: \frac{48}{(x + y)} + \frac{40}{(x - y)} ...(2)}$

$\sf{let \: the \: \frac{1}{x + y} = a \: and \: \frac{1}{x - y} = b }$

$\sf{ \therefore \: 36a + 32b = 7..(1)}$

$\sf{48a + 40b = 9..(2)}$

$\sf{multiplying \: {eq}^{n} \: (1) \: and (2)}$

$\sf{ 192a + 160b = 36}...(3)$

$\sf{180a - 160b = 35..(4)}$

$\sf{subtract \: 4 \: from \: 3 \: we \: get}$

$\sf{a = \frac{1}{12} and \: b \: = \frac{1}{8} }$

$\sf{ \therefore \: \frac{1}{(x + y)} = a = \frac{1}{12} \rightarrow \: (x + y) = 12..(5)}$

$\sf{ \therefore \: \frac{1}{(x - y)} = b = \frac{1}{8} \rightarrow \: (x - y) = 8...(6)}$

$\sf{after \: adding \: 5 \: and \: 6}$

$\sf{x = 10 \: and \: y = 2}$

$\sf{ \therefore \: speed \: of \: the \: boat \: in \: downstream = 10}$

$\sf{ \: speed \: of \: the \: boat \: in \: upstream = 2}$

$\sf{ \qquad \: \: \: \: \: \: { \underline{ hope \: it \: helps \: you \: \ddot \smile}}}$

Answer 2

Answer:

Newton's first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. This postulate is known as the law of inertia.