Brain-Teaser 470

From The Sunday Times, 31st May 1970 [link]

Joseph’s garage, built at ground level on to the side wall of his house, had uniform external dimensions of (exactly) 10 ft. high by 10 ft. wide.

Wishing to paint from the outside a top-floor window-frame over the garage, he positioned his longest ladder (whose length was over 30 ft.) with its foot on the ground at such a distance from the garage that its top rested against the house wall at the maximum height possible.

Discovering, however, that despite this he could not reach up to the window, he borrowed his neighbour Jacob’s ladder and, positioning it similarly, found that he could now reach comfortably.

With either ladder the length, distance and height referred to were all integral numbers of inches.

How much longer was Jacob’s ladder than Joseph’s, and how much higher on the wall did it reach?

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