tmua.me Medium Set E Paper 2 · Question 18

A train is $120\,\mathrm{m}$ long. At a constant speed it takes $30$ seconds to pass completely past a straight platform.

At three-quarters of that speed, it takes $64$ seconds to pass completely past a second straight platform, whose length is twice that of the first.

Each time is measured from the instant the front of the train reaches the near end of the platform until the rear leaves the far end.

What is the length of the first platform?

90\,\mathrm{m}

300\,\mathrm{m}

360\,\mathrm{m}

480\,\mathrm{m}

180\,\mathrm{m}

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