rate speed

Question

A boat can travel 29 mph in still water. If the boat can travel 100 miles with the current in the same time it can travel 80 miles against the current, find the rate of the current r in miles per hour. (Enter an exact number as an integer, fraction, or decimal.)

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  Usually, with such problems, there are two objects or situations which relate one of the variables, or else the variable is constant.  That way, we can solve the problem.  In this problem, the Time ("in the same time") is constant, so we can form an equation and set two expressions equal.

 

If D=RT, then:  T=D/R

 

So,   time with current   =  time against current

  T = (100) / (29 + r)    =     (80) / (29 - r)

 

O.K., what's r?

Answer 2

Think about how far the boat can travel without the current. Distance = velocity * time. That gets you a basis for what is going on. Now, if the current is opposing the boat, does it travel faster or slower compared to the original boat velocity? What about if the current is in the same direction as the motion of the boat? Use these situations to write equations for the total velocity of the boat. Good luck!