Question

a train travels 360 km at a uniform speed .if speed had been 5km/h more,it would have taken 1 hour less for the same journey. find speed of train

Answer 1

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ʟᴇᴛ ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ ʙᴇ x ᴋᴍ/ʜ.

ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴄᴏᴠᴇʀ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 360 ᴋᴍ
=  360/x ʜᴏᴜʀs.

ɴᴇᴡ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ
= (x+5) ᴋᴍ/ʜ.

ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴄᴏᴠᴇʀ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 360 ᴋᴍ ᴀᴛ ɴᴇᴡ sᴘᴇᴇᴅ
= 360/x+5 ʜᴏᴜʀs.

ᴛʜᴇ ᴛʀᴀɪɴ ᴛᴀᴋᴇs 1 ʜᴏᴜʀ ʟᴇss ᴛɪᴍᴇ

∴ 360/x - 360/ x+5 = 1

⇒360 (x+5-x)/x(x+5) = 1
⇒360 (5) = x² + 5x
⇒1800 = x² + 5x
⇒x² + 5x - 1800 = 0
⇒x² + 45x - 40x - 1800 = 0

⇒x (x+45) - 40( x +45) = 0
⇒(x+45) (x-40) = 0

⇒x = (-45), 40

ʙᴜᴛ sɪɴᴄᴇ sᴘᴇᴇᴅ ᴄᴀɴɴᴏᴛ ʙᴇ ɪɴ ɴᴇɢᴀᴛɪᴠᴇ.
∴ x = 40 ᴋᴍ/ʜʀ.


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Answer 2

answer is in pics hope it was helpful