A square has side length 100 m. An and Binh start simultaneously at opposite vertices and walk anticlockwise along its sides. An walks at 50 m/min and Binh at 40 m/min. At each vertex An rests for 1 minute and Binh for 2 minutes. After how many minutes does An first catch Binh?
A rectangular fish tank has a 15 dm by 8 dm base and height 12 dm. Its current water depth is 5 dm. How many litres must be added so that water occupies 80% of its volume?
In triangle ABC, angle A=2 angle B=6 angle C. Points D on BC and E on AC satisfy DA=DB=DE. Draw EH perpendicular to BC, with H on BC, and let I=AD∩BE. Find angle AIH. The illustration is not to be measured.
The hanging mobiles in the diagram are balanced. Ignore the mass of the bars and strings. The total mass of the suspended objects is 112 g. What is the mass of one star, in grams?
The first traveller takes 3 hours from A to B at constant speed v. The second travels from A to B, sometimes at 2 v and sometimes at v/3, arriving after 5 hours. For how many minutes does the second travel at 2 v?
Two motorcyclists start simultaneously from A and B towards each other. The first reaches B and turns back; the second reaches A and turns back immediately. Their first meeting is 15 km from A and their second is 9 km from B, with opposite directions at the second meeting. Find AB in kilometres.
The diagram is a 4×4 square grid from A at the lower-left corner to B at the upper-right. An travels from A using only up and right steps; Binh travels from B using only down and left steps. They start simultaneously with the same speed. In how many different ways can they meet?
A 3×4 table has the fixed entries shown. Which number must be removed from 0,2,3,4,5,7,8,10,11 so that the remaining eight numbers can fill the blank cells and every row and column has the same arithmetic mean? Explain why.
Rectangle ABCD is divided into rectangles(1) and(2), as shown. The perimeter of(2) is twice that of(1), and its area is four times that of(1). Find AD in centimetres, given AB=10 cm.
An attraction has four gates: East, West, South, North. Visitors A and B enter simultaneously and exit simultaneously. The probability that each exits through a gate different from their own entrance, and that they do not meet at either the entrance or exit, is a/b in lowest terms. Find a+b.
Tom is 100 m behind Jerry and expects to catch him in 20 seconds. When the gap reaches 15 m, Jerry triples his initial speed. Tom keeps his speed and catches Jerry 2 seconds later than originally expected. Find Tom’s initial speed in m/s.
