SOLUTION: A boat travels 2 km upstream and 2km back. The time for the round trip is 8hrs. The speed of the stream is 3km/ hr. What is the speed of the boat in still water? Round the answer

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A boat travels 2 km upstream and 2km back. The time for the round trip is 8hrs. The speed of the stream is 3km/ hr. What is the speed of the boat in still water? Round the answer       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 803108: A boat travels 2 km upstream and 2km back. The time for the round trip is 8hrs. The speed of the stream is 3km/ hr. What is the speed of the boat in still water?
Round the answer to the nearest hundredth. Type an integer or a decimal.
The speed of the boat is 3.26km/ hr.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hrs for going upstream
+8+-+t+ = the time in hrs for going downstream
Let +b+ = the speed of the boat in still water
---------------
Going upstream:
(1) +2+=+%28+b+-+3+%29%2At+
Going downstream:
(2) +2+=+%28+b+%2B+3+%29%2A%28+8+-+t+%29+
-------------------------
(2) +2+=+8b+%2B+24+-+b%2At+-+3t++
(2) +2+=+b%2A%28+8+-+t+%29+%2B+24+-+3t+
and
(1) +2+=+b%2At+-+3t+
(1) +b%2At+=+2+%2B+3t+
(1) +b+=+%28+2+%2B+3t+%29+%2F+t+
----------------------
By substitution:
(2) +2+=+%28%28+2+%2B+3t+%29+%2F+t+%29%2A%28+8+-+t+%29+%2B+24+-+3t+
(2) +3t+=+%28%28+2+%2B+3t+%29+%2F+t+%29%2A%28+8+-+t+%29+%2B+22+
Multiply both sides by +t+
(2) +3t%5E2+=+%28+2+%2B+3t+%29%2A%28+8+-+t+%29+%2B+22t+
(2) +3t%5E2+=+16+%2B+24t+-+2t+-+3t%5E2+%2B+22t+
(2) +6t%5E2+-+44t+-+16+=+0+
(2) +3t%5E2+-+22t+-+8+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+-22+
+c+=+-8+
+t+=+%28+-%28-22%29+%2B-+sqrt%28+%28-22%29%5E2+-+4%2A3%2A%28-8%29+%29%29+%2F+%282%2A3%29+
+t+=+%28+22+%2B-+sqrt%28+484+%2B+96+%29%29+%2F+%282%2A3%29+
+t+=+%28+22+%2B-+sqrt%28+580+%29%29+%2F+6+
+t+=+%28+22+%2B+24.083+%29+%2F+6+
+t+=+46.083+%2F+6+
+t+=+7.681+ hrs
and, since
(1) +b+=+%28+2+%2B+3t+%29+%2F+t+
(1) +b+=+%28+2+%2B+3%2A7.681+%29+%2F+7.681+
(1) +b+=+25.042+%2F+7.681+
(1) +b+=+3.26+
The speed of the boat in still water is 3.26 km/hr
---------------
check:
(2) +2+=+%28+b+%2B+3+%29%2A%28+8+-+t+%29+
(2) +2+=+%28+3.26+%2B+3+%29%2A%28+8+-+7.681+%29+
(2) +2+=+6.26+%2A+.319+
(2) +2+=+1.997+
error due to rounding off
OK