Question

A train travels 360 km at a uniform speed if the speed had been 5 km per hour more it would have taken 1 hour less for the same journey find the speed of the train​

Answer 1

Answer:

40km/hr

Step-by-step explanation:

let the velocity of the train be x km/hr

∴Time taken in the first case=(360÷x) hr

& Time taken in the second case is= (360÷(x+5)) hr

∴According to the question,

(360÷x) - (360÷(x+5))= 1

→ x²+5x-1800=0

→x=-45 or x=40

∵x=-45(ignored)

∴x=40

Answer 2

ʜᴇʏᴀ ᴍᴀᴛᴇ!!

ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ ⏬ ⏬

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.

sɪɴᴄᴇ, 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.

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴏʀɪɢɪɴᴀʟ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ ɪs 40 ᴋᴍ/ʜ.