# maths help?

a) Person x is standing at position A and person y is standing at position B which is 40km away from A along a straight road. Persons x and y move towards each other at a speed of 4km/h and 16km/h respectively. y starts 1 hour after x started traveling. i) after how many hours will x meet y? ii) determine how far from position A they will meet

b) a river with straight banks flows at a speed of 4 km/h. a person wishes to swim from point P to Q directly oposite on the other side of the river. the person can swim at 8km/h in still water. find the direction the person should swim so that the person can go from point A to point B.

Favorite Answer

a) After 1 hour, X has moved 4km from position A. X and Y are therefore now 36km apart. They are closing towards each other at 20km/h, therefore they take 36/20 = 1.8 hrs or 1 hr 48 mins to meet. X has now been travelling for 2.8 hrs at 4km per hour, therefore they meet at a point 4 x 2.8 = 11.2 km from A.

b) Here you need to imagine a triangle with P and Q as two corners, and a third corner, nominally X, which is the point upstream that the swimmer should point at in order to end up at Q. (I’m assuming your reference to A and B at the end is an error.)

Then the vector PX is the direction that the swimmer should head in at 8km/h to end up at Q. Vector XQ is 4km/h effect of current. So angle XPQ (the angle off direct PQ that the swimmer should head) is arc sin (4/8) = arc sin 0.5 = 30 degrees.

Good luck, and hope this all makes sense!

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