algebra word problem

Question

A sailboat travels 12 miles downstream in only 2 hours. The return trip upstream takes 3 hours. Find the speed of the sailboat in still water and the rate of the current.

Answer 1

Step 1: We know that distance = rate*time (or d = r*t)

Step 2: Therefore we can solve this relation for r to get (r = d/t)

Step 3: For the boat going downstream: rate = 12mi/2hr = 6mi/hr

Therefore, the rate of the boat (r) plus the rate of the current (c) will = 6mi/hr. Thus r + c = 6 [eq 1]

Step 4: For the boat going upstream: rate =12mi/3hr = 4mi/hr

Therefore, the rate of the boat (r) minus the rate of the current (c) will = 4mi/hr. Thus r - c = 4 [eq 2]

Step 5: We now need to solve [eq 1] and [eq 2] simultaneously (at the same time) to determine c and r.

Simply add both left add right sides of both equations to get: (r + r)+ (c + -c) = 6 + 4

Which simplifies to 2r = 10, which means that r = 10/2 or r = 5.

This means that the boat rate is 5mi/hr. Therefore in still water, the boat will travel at 5mi/hr

Step 6: To find the rate of the current, we can simply plug in 5 for r in either equation, and then solve for c.

Choosing [eq 1],

r + c = 6

5 + c = 6

c = 6 - 5

c = 1

Therefore, the rate of the current is 1mi/hr.