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Question
A man completed a trip of 136 km in 8 hours. Some part of the trip was covered at 15 km/hr and the remaining at 18 km/hr. Find the part of the trip covered at 18 km/hr.
Solution
Total distance of the trip = 136 km
Let part of the trip covered at 18 km/hr = x km
∴ Distance of the trip covered at 15 km/hr = (136 - x)km
Time taken by the man to cover x km = `"Distance"/"speed" = "x"/18` hours
Time taken by the man to cover (136 - x) km = `(136 - "x")/15` hours
Time taken by the man to cover a trip of 136 km = 8 hours
`therefore "x"/18 + (136 - "x")/15 = 8`
`=> "x"/18 xx 90 + (136 - "x")/15 xx 90 = 8 xx 90`
....[Multiplying each term by 90 becuase L.C.M. of denominatorsn = 90]
⇒ 5x + 6 (136 - x) = 720
⇒ 5x + 816 - 6x = 720
⇒ 5x - 6x = 720 - 816
⇒ -x = -96
⇒ x = 96
∴ Part of the trip covered at 18 km/hr = 96 km
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