SOLUTION: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of

Algebra ->  Expressions-with-variables -> SOLUTION: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of      Log On


   

Question 780612: Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of the river is 5 km per hr, what was her boat speed in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in km/hr in still water
Let +d+ = the one-way distance the boat travels in km
Going upstream:
+d+=+%28+s+-+5+%29%2A%281%2F2%29+
Going downstream:
+d+=+%28+s+%2B+5%29%2A%2810%2F60%29+
----------------------
By substitution:
+%28+s+-+5+%29%2A%281%2F2%29++=++%28+s+%2B+5%29%2A%281%2F6%29+
Multiply both sides by +6+
+3%2A%28+s+-+5+%29+=+s+%2B+5+
+3s+-+15+=+s+%2B+5+
+2s+=+20+
+s+=+10+
The speed of the boat in still water is 10 km/hr
check:
+d+=+%28+s+-+5+%29%2A%281%2F2%29+
+d+=+%28+10+-+5+%29%2A%281%2F2%29+
+d+=+5%2F2+ km
and
+d+=+%28+s+%2B+5%29%2A%281%2F6%29+
+d+=+%28+10+%2B+5+%29%2A%281%2F6%29+
+d+=+15%2F6+
+d+=+5%2F2+ km
OK