Question 1179660
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After using the given information to find that the speed with the current is 12 mph and the speed against the current is 6 mph, the other tutors solved the problem with formal algebra by using a pair of equations involving the boat speed and the current speed.<br>
Of course, a formal algebraic solution is possibly what was required.<br>
However, this kind of problem is so common that, if formal algebra is not required, it can be solved informally with very little effort using logical reasoning.<br>
If the current speed added to the boat speed is 12 mph and the current speed subtracted from the boat speed is 6 mph, then logical reasoning says that the boat speed is halfway between 12 mph and 6mph -- i.e., 9 mph -- and the current speed is then the difference between 9 mph and either 6 mph of 12 mph.<br>
ANSWERS:
boat speed: 9 mph (halfway between 6 mph and 12 mph)
current speed: 12-9 = 3 mph; or 9-6 = 3 mph<br>