Question

15. A person rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40
km upstream as in going 40 km downstream. Find the speed of the stream. (3)​

Answer 1

$\huge \mathscr{\orange {\underline{\pink{\underline {Answer:-}}}}}$

Consider,

Speed of rowing by a person =5 km/hr.

Speed of stream =x km/hr

Upstream Speed  =(5−x) km/hr

Downstream speed =(5+x) km/hr

According to the question,

⇒40/5−x = 3×40/5+x

⇒5+x = 15−3x

⇒4x = 10

⇒x = 2.5 km/hr

Answer 2

Answer:

ʟᴇᴛ’s ᴀssᴜᴍᴇ x ᴛᴏ ʙᴇ ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ sᴛʀᴇᴀᴍ.

sᴏ, ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

sᴘᴇᴇᴅ ᴏғ ʙᴏᴀᴛ ɪɴ ᴅᴏᴡɴsᴛʀᴇᴀᴍ = (5 + x) ᴀɴᴅ,

sᴘᴇᴇᴅ ᴏғ ʙᴏᴀᴛ ɪɴ ᴜᴘsᴛʀᴇᴀᴍ = (5 – x)

ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ,

ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ɪɴ ᴏɴᴇ ᴡᴀʏ ɪs 40 ᴋᴍ.

ᴀɴᴅ,

ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴅᴜʀɪɴɢ ᴜᴘsᴛʀᴇᴀᴍ = 3 × ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴅᴜʀɪɴɢ ᴛʜᴇ ᴅᴏᴡɴsᴛʀᴇᴀᴍ

ᴇxᴘʀᴇssɪɴɢ ɪᴛ ʙʏ ᴇϙᴜᴀᴛɪᴏɴs, ᴡᴇ ʜᴀᴠᴇ

40/ (5 – x) = 3 x 40/ (5 + x) [∵ ᴛɪᴍᴇ = ᴅɪsᴛᴀɴᴄᴇ/ sᴘᴇᴇᴅ]

ʙʏ ᴄʀᴏss ᴍᴜʟᴛɪᴘʟɪᴄᴀᴛɪᴏɴ, ᴡᴇ ɢᴇᴛ

(5+x) = 3(5-x)

⇒ 5 + x = 3(5 – x)

⇒ x + 3x = 15 – 5

⇒ x = 10/4 = 2.5

ᴛʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ sᴛʀᴇᴀᴍ ɪs 2.5 ᴋᴍ/ʜʀ.