ANSWERS: 1
  • Let V be the canoeist's speed on the first part of the trip. Time = distance / speed So T1 = time on first part = 63 / V and T2 = time on 2nd part = 6 / (V-5) T1 + T2 = 5 So 63/V + 6/(V-5) = 5 This is the equation you must solve for V. Common denominator is V*(V-5); multiply both sides by it: 63(V-5) + 6V = 5V(V-5) expand: 63V - 315 + 6V = 5V^2 - 25V collect terms: 5V^2 - 94V + 315 = 0 Solve using the quadratic formula. I used a website calculator here: http://www.math.com/students/calculators/source/quadratic.htm One root is negative and should be discarded. The other root is V = 14.4+ So 14.4 mph on the first part, 9.4 mph on 2nd part. Plug back in to the problem -- it checks -- approximately. You might be required to give an exact formula in terms of radicals, in which case forget the quadratic calculator & work it out exactly.

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