JMC 2017 Challenge cont.

21. The small trapezium on the right has three equal sides and angles of 60° and 120°. Nine copies of this trapezium can be placed together to make a larger version of it, as shown.

The larger trapezium has perimeter 18 cm. What is the perimeter of the smaller trapezium?

23. The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer.

Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark.

How many cells have more than 1 mark?

25. The distance between Exeter and London is 175 miles. Sam left Exeter at 10:00 on Tuesday for London. Morgan left London for Exeter at 13:00 the same day. They travelled on the same road. Up to the time when they met, Sam's average speed was 25 miles per hour, and Morgan's average speed was 35 miles an hour.

At what time did Sam and Morgan meet?

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