Question

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river? ​

Answer 1

S1*t1 = 1400 : S1 speed of boat 1, t1 : time to do 1400 meters(boat 1) 1400 + S2*t1 = X : S2 speed of boat 2 S1*t2 = X + 600 : t2 time to do X + 600 (boat 2) S2*t2 = 2X - 600 S1 = 1400/t1 S2 = (X-1400)/t1 T = t2/t1 : definition substitute S1, S2 and t2/t1 using the above expressions in equations 3 and 4 to obtain 1400*T = X + 600 X*T - 1400*T = 2X - 600 : 2 equations 2 unknowns Eliminate T and solve for X to obtain X = 3600 meters.

Answer 2

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the solutions to the equation you provide are not in R. I think it is because boat1 did not travel 1400−x to the first meeting, it traveled x−1400. Similarly, to the second meeting the boats have traveled x+600 and 2x−600 respectively. Using 1400, x−1400, x+600 and 2x−600 provides correct answer

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