SOLUTION: A boat went a certain distance up a river and back in 2 hours and 56 minutes. Its speed was 17.5 mph going upriver and 21 mph returning. How far up the river did it go ? can you p

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A boat went a certain distance up a river and back in 2 hours and 56 minutes. Its speed was 17.5 mph going upriver and 21 mph returning. How far up the river did it go ? can you p      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 937832: A boat went a certain distance up a river and back in 2 hours and 56 minutes. Its speed was 17.5 mph going upriver and 21 mph returning. How far up the river did it go ?
can you please give an equation and detailed explanation
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance ( up or down river )
Let +t+ = time in hrs to go upriver
-----------------------------------
Convert +56+ min to hours
+56%2F60+=+.9333+ hrs
+2.9333+-+t+ = time in hrs to go downriver
-----------------------------------------
Equation for going upstream:
(1) +d+=+17.5t+
Equation for going downstream:
(2) +d+=+21%2A%28+2.9333+-+t+%29+
----------------------------
Substitute (1) into (2)
(2) +17.5t+=+21%2A%28+2.9333+-+t+%29+
(2) +17.5t+=+61.6+-+21t+
(2) +38.5t+=+61.6+
(2) +t+=+1.6+ hrs
Plug this result back into (1)
(1) +d+=+17.5%2A1.6+
(1) +d+=+28+
The boat went 28 mi upriver
---------------------------
check:
(2) +d+=+21%2A%28+2.9333+-+t+%29+
(2) +28+=+21%2A%28+2.9333+-+1.6+%29+
(2) +28+=+61.6+-+33.6+
(2) +28+=+28+
OK