SOLUTION: A motorboat can maintain a constant speed of 16mph relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the trip takes 15 minutes. What is the cu

Algebra ->  Test -> SOLUTION: A motorboat can maintain a constant speed of 16mph relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the trip takes 15 minutes. What is the cu      Log On


   

Question 678025: A motorboat can maintain a constant speed of 16mph relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the trip takes 15 minutes. What is the current's speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
+16+-+c+ = the boat's speed going upstream
+16+%2B+c+ = the boat's speed going downstream
given:
Going upstream:
(1) +d+=+%28+16+-+c+%29%2A%281%2F3%29+
Going downstream:
(2) +d+=+%28+16+%2B+c+%29%2A%281%2F4%29+
------------------------
Substitute (1) into (2)
+%28+16+-+c+%29%2A%281%2F3%29+=+%28+16+%2B+c+%29%2A%281%2F4%29+
Multiply both sides by +12+
+4%2A%28+16+-+c+%29+=+3%2A%28+16+%2B+c+%29+
+64+-+4c+=+48+%2B+3c+
+7c+=+16+
+c+=+16%2F7+
+c+=+2.286+
The current's speed is 2.286 mi/hr