Car X started from town M at 6 a.m. and went towards town N. Car Y started from M at 7 a.m. in the same direction as X. It overtook X after covering 40% of the distance MN. Both cars then continued travelling towards N. On reaching N, Y turned back immediately and crossed X after covering 12% of the distance NM. Find the time taken by car Y to cover the distance MN.5 hours7.5 hours4.5 hours6 hours
Question
Car X started from town M at 6 a.m. and went towards town N. Car Y started from M at 7 a.m. in the same direction as X. It overtook X after covering 40% of the distance MN. Both cars then continued travelling towards N. On reaching N, Y turned back immediately and crossed X after covering 12% of the distance NM. Find the time taken by car Y to cover the distance MN.5 hours7.5 hours4.5 hours6 hours
Solution
The problem can be solved by following these steps:
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Let's denote the speed of car X as Vx and the speed of car Y as Vy. Also, let's denote the distance between towns M and N as D.
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According to the problem, car Y overtook car X after covering 40% of the distance. This means that car X covered 40% of the distance in 1 hour more time than car Y. We can write this as: 0.4D/Vx = 0.4D/Vy + 1.
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Simplifying the equation, we get Vy/Vx = 1.4.
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After reaching town N, car Y turned back and crossed car X after covering 12% of the distance. This means that car X covered 88% of the distance while car Y covered 112% of the distance in the same time. We can write this as: 0.88D/Vx = 1.12D/Vy.
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Simplifying the equation, we get Vy/Vx = 0.88/1.12 = 0.7857.
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Now we have two equations for Vy/Vx, which should be equal. So, we can write 1.4 = 0.7857, which is not possible.
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Therefore, there seems to be a mistake in the problem as it is not possible to find a consistent solution with the given conditions.
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