MathDB

5

Part of ICMC 3

Problems(1)

ICMC 2019/20 Round 1, Problem 5

Source: Imperial College Mathematics Competition 2019/20 - Round 1

8/7/2020
A particle moves from the point PP to the point QQ in the Cartesian plane. When it passes through any point (x,y)(x,y), the particle has an instantaneous speed of x+y\sqrt{x + y}. Compute the minimum time required for the particle to move:
(i) from P1=(−1,0)P_1=(-1,0) to Q1=(1,0)Q_1=(1,0), and
(ii) from P2=(0,1)P_2=(0,1) to Q2=(1,1)Q_2=(1,1).
proposed by the ICMC Problem Committee
college contests