Math Question - Algebra

Question

A scenic road around Lake Rotorua is I I miles in length. Tom leaves the hotel on his bike averaging 10 mph and heads west around the lake. Bill leaves at the same time and heads in the opposite direction at 45 mph. How far from the hotel will Tom have traveled when they meet?

Answer 1

11 miles around the Lake

Tom leaves heading west around the lake at 10 mph

Bill leaves at same time heading east around the lake at 45 mp

how far from the hotel will Tom be when they meet??

11/(10 +45) = 11/55 = 1/5 hr = 12 minutes when they meet

in 1/5 of an hour Tom wen 10x1/5 = 2 miles, from the hotel, on the curvature of the lake

as the crow flies, the distance is at about 2 miles, but depends on how curved the lake in that 2 mile stretch

let's say the lake is a perfect circle, then the distance to the hotel is shorter. It's chord length with an angle of 360/5 = 132 degrees, the arc = 2 miles, the chord = the straight line distance to the hotel arc/chord ratio = about 1.2609. chord = 1.2609(2 miles) = 2.5218 miles to the hotel from where Tom met up with Bill