Question

A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return
the same spot. Find the speed of the stream.​

Answer 1

Answer:

speed of boat 24 kmph=x

speed of steam=y find

now

now total distance = 32 km

time taken = distance ÷ speed

while in upstream

time will be z+1= 32÷ x-y

while in down stream

time will be z= 32÷ x+y

so we get two eq

1. z= 32÷24+y

2.z=(32÷24-y)-1

now equate both equation

wait solving equations

i got speed = 8km per hour

and equation by equating both eq is 24^2 -x^2=64x

hope it help

plz mark branliest

Answer 2

$\large{\mathcal{\underline{\red{ANSWER:}}}}\\ \\ \\ {\underline{\bf Given:}}\\ \\ \longrightarrow\sf Speed\;of\;boat\;in\;still\;water=24\;km/h\\ \\ \longrightarrow\sf Total\;distance=32\;km\\ \\ \\ {\underline{\bf To\;Find:}}\\ \\ \longrightarrow\sf Speed\;of\;stream.$

${\underline{\sf Now,\;let\;the\;speed\;of\;the\;stream\;be\;x\;km/h.}}$

${\underline{\bf Case\;1\;:In\;Upstream}}\\ \\ \longrightarrow\sf Speed\;of\;the\;boat\;in\;upstream=Speed\;of\;boat\;in\;still\;water\;-\;Speed\;of\;the\;stream\\ \\ \longrightarrow\sf Speed\;of\;the\;boat\;in\;upstream= (24-x)\;km/h\\ \\ \rule{200}{2}\\ \\ {\underline{\bf Case\;2\;:In\;Downstream}}\\ \\ \longrightarrow\sf Speed\;of\;the\;boat\;in\;downstream=Speed\;of\;boat\;in\;still\;water\;+\;Speed\;of\;the\;stream\\ \\ \longrightarrow\sf Speed\;of\;the\;boat\;in\;downstream= (24+x)\;km/h$$\rule{200}{2}$

$\therefore \sf Time\;of\;upstream\;journey = Time\;for\;downstream\;journey + 1\;hr\\ \\ \\ \longrightarrow \bf We\;know\;that,\;Time=\dfrac{Distance}{Speed}\\ \\ \\ \therefore \sf \dfrac{Distance\;covered\;in\;upstream}{Speed\;of\;boat\;in\;upstream}= \dfrac{Distance\;covered\;in\;downstream}{Speed\;of\;boat\;in\;downstream}+1\;hr\\ \\ \\ {\underline {\bf Now,\;put\;the\;values,}}$

$\longrightarrow \sf \dfrac{32}{24-x}=\dfrac{32}{24+x}+1\\ \\ \\ \longrightarrow \sf \dfrac{32}{24-x}-\dfrac{32}{24+x}=1\\ \\ \\ \longrightarrow \sf \dfrac{768+32x-768+32x}{(24-x)(24+x)}=1\\ \\ \\ \longrightarrow \sf \dfrac{64x}{(24)^{2}-(x)^{2}}=1\\ \\ \\ \longrightarrow \sf \dfrac{64x}{576-x^{2}}=1\\ \\ \\ \longrightarrow \sf 64x=576-x^{2}\\ \\ \\ \longrightarrow \sf x^{2}+64x-576=0$

${\underline{\bf Now,\;by\;using\;splitting\;middle\;term\;method\;we\;will\;solve\;it,}}\\ \\ \longrightarrow \sf x^{2}+64x-576=0\\ \\ \\ \longrightarrow \sf x^{2}+72x-8x-576=0\\ \\ \\ \longrightarrow \sf x(x+72)-8(x+72)=0\\ \\ \\ \longrightarrow \sf (x-8)(x+72)=0\\ \\ \rule{100}{2}\\ \\ \longrightarrow \sf x-8=0\\ \\ \longrightarrow \sf x=8\;km/h\\ \\ \rule{100}{2} \\ \\ \longrightarrow \sf x+72=0\\ \\ \longrightarrow \sf x=-72\;km/h$

${\underline{\bf We\;know\;that,\;Speed\;cannot\;be\;negative,}}\\ \\ \\ {\boxed{\boxed{\bf{\therefore Speed\;of\;the\;stream=8\;km/h.}}}}$