Question

on a 120 km track, a train travels the first 30 km at a uniform speed of 30km/hr. How fast must the train travel the next 90km so as to average 60km/hr for the entire trip?

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Answer 1

╰☆☆ ʜᴇʏᴀ ᴍᴀᴛᴇ ☆☆╮

please refer to the attachment

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Answer 2

Tᴏᴛᴀʟ ᴅɪsᴛᴀɴᴄᴇ = 120 ᴋᴍ

Iɴɪᴛɪᴀʟ ᴅɪsᴛᴀɴᴄᴇ ᴄᴏᴠᴇʀᴇᴅ = 30 ᴋᴍ

Sᴘᴇᴇᴅ ʙʏ ᴡʜɪᴄʜ ɪɴɪᴛɪᴀʟ ᴅɪsᴛᴀɴᴄᴇ ᴄᴏᴠᴇʀᴇᴅ = 30 ᴋᴍ/ʜʀ

Tʜᴇʀᴇғᴏʀᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴄᴏᴠᴇʀ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 30 ᴋᴍ = 1 ʜʀ

Aᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ ɴᴇᴇᴅᴇᴅ ғᴏʀ ᴛʜᴇ ᴇɴᴛɪʀᴇ ᴛʀɪᴘ = 60 ᴋᴍ/ʜʀ

Tᴏᴛᴀʟ ᴛɪᴍᴇ ᴛᴏ ʙᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴄᴏᴠᴇʀ 120 ᴋᴍ = 120/60 = 2 ʜᴏᴜʀs

Rᴇᴍᴀɪɴɪɴɢ ᴅɪsᴛᴀɴᴄᴇ ᴛᴏ ʙᴇ ᴄᴏᴠᴇʀᴇᴅ = 120 - 30 = 90 ᴋᴍ

Tɪᴍᴇ ᴛᴏ ʙᴇ ᴛᴀᴋᴇɴ ᴛᴏ ᴄᴏᴠᴇʀ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 90 ᴋᴍ = 2 ʜʀ - 1 ʜʀ 

= 1 ʜᴏᴜʀ

Tʜᴇʀᴇғᴏʀᴇ, sᴘᴇᴇᴅ ɴᴇᴇᴅᴇᴅ ғᴏʀ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ᴅɪsᴛᴀɴᴄᴇ ᴏғ 90 ᴋᴍ = 90 ᴋᴍ/ʜʀ

Hᴇɴᴄᴇ, ᴛʜᴇ ᴛʀᴀɪɴ ᴍᴜsᴛ ᴛʀᴀᴠᴇʟ ᴛʜᴇ ɴᴇxᴛ 90 ᴋᴍ ᴀᴛ ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ 90 ᴋᴍ/ʜʀ sᴏ ᴀs ᴛᴏ ʜᴀᴠᴇ ᴀɴ ᴀᴠᴇʀᴀɢᴇ ᴏғ 60 ᴋᴍ/ʜʀ ғᴏʀ ᴛʜᴇ ᴇɴᴛɪʀᴇ ᴊᴏᴜʀɴᴇʏ.