SOLUTION: To deliver a message, an army officer will travel by auto at 75 miles per hour from A to B, and then by airplane to C against a wind blowing 40 miles per hour. The airplane can fly

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: To deliver a message, an army officer will travel by auto at 75 miles per hour from A to B, and then by airplane to C against a wind blowing 40 miles per hour. The airplane can fly      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 987665: To deliver a message, an army officer will travel by auto at 75 miles per hour from A to B, and then by airplane to C against a wind blowing 40 miles per hour. The airplane can fly 280 miles per hour in still air. If the messanger takes 3 2/3 hours in going from A to C, and 3 1/6 hours for the return trip, what is the distance from A to C?
Found 3 solutions by MathTherapy, macston, josmiceli:
Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

To deliver a message, an army officer will travel by auto at 75 miles per hour from A to B, and then by airplane to C against a wind blowing 40 miles per hour. The airplane can fly 280 miles per hour in still air. If the messanger takes 3 2/3 hours in going from A to C, and 3 1/6 hours for the return trip, what is the distance from A to C?
Distance from A to C: 125 + 480, or highlight_green%28605%29 miles 


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
X=distance from A to B; Y=distance from B to C
Speed against wind (from B to C) =280mph-40mph=240mph
Speed with wind (from C to B)=280mph+40mph=320mph
.
X%2F75mph%2BY%2F240mph=3.667hrs
X%2F75mph%2BY%2F320mph=3.167hrs
.
X%2F75mph%2BY%2F240mph-0.5hr=X%2F75mph%2BY%2F320mph
Y%2F240mph-0.5hr=Y%2F320mph
1.33Y-160=Y
0.33Y=160
Y=480 The distance from B to C is 480 miles.
.
X%2F75mph%2BY%2F240mph=3.667hrs
X%2F75mph%2B480mi%2F240mph=3.667hrs
X%2F75mph%2B2hrs=3.667hrs
X%2F75mph=1.67hrs
X=%281.667hrs%29%2875mph%29
X=125miles The distance from A to B is 125 miles.
.
Distance from A to C=(distance from A to B)+(distance from B to C)
Distance from A to C=125 miles+480 miles=605 miles
ANSWER: The distance from A to C is 605 miles.
.
CHECK:
X%2F75mph%2BY%2F320mph=3.167hrs
125mi%2F75mph%2B480mi%2F320mph=3.167hrs
1.667hrs%2B1.5hrs=3.167hrs
3.167hrs=3.167hrs

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let distance AB = +d%5B1%5D+ in miles
Let distance BC = +d%5B2%5D+ in miles
Distance AC = +d%5B1%5D+%2B+d%5B2%5D+ miles
----------------------------
Let +t%5B1%5D+ = time in hrs to travel distance +d%5B1%5D+
Let +t%5B2%5D+ = time in hrs to travel distance +d%5B2%5D+ ( going )
Let +t%5B3%5D+ = time in hrs to travel distance +d%5B2%5D+ ( returning )
-----------------------------
+t%5B1%5D+%2B+t%5B2%5D+=+11%2F3+
+t%5B1%5D+%2B+t%5B3%5D+=+19%2F6+
-----------------------------
+d%5B1%5D+=+75%2At%5B1%5D+
+d%5B2%5D+=+%28+280+-+40+%29%2At%5B2%5D+
and, returning:
+d%5B1%5D+=+75%2At%5B1%5D+
+d%5B2%5D+=+%28+280+%2B+40+%29%2At%5B3%5D+
---------------------------
There are 5 unkowns and 5 equations,
so it is solvable
---------------------------
+t%5B2%5D+=+11%2F3+-+t%5B1%5D+
+t%5B3%5D+=+19%2F6+-+t%5B1%5D+
----------------------
+d%5B2%5D+=+%28+280+-+40+%29%2At%5B2%5D+
+d%5B2%5D+=+240%2A%28+11%2F3+-+t%5B1%5D+%29+
----------------------------
+d%5B2%5D+=+320%2A%28+19%2F6+-+t%5B1%5D+%29+
----------------------------
+240%2A%28+11%2F3+-+t%5B1%5D+%29+=+320%2A%28+19%2F6+-+t%5B1%5D+%29+
+880+-+240t%5B1%5D+=+3040%2F3+-+320t%5B1%5D+
+80t%5B1%5D+=+3040%2F3+-+2640%2F3+
+80t%5B1%5D+=+400%2F3+
+t%5B1%5D+=+5%2F3+ hrs
and
+t%5B2%5D+=+11%2F3+-+t%5B1%5D+
+t%5B2%5D+=+11%2F3+-+5%2F3+
+t%5B2%5D+=+2+ hrs
and
+t%5B3%5D+=+19%2F6+-+t%5B1%5D+
+t%5B3%5D+=+19%2F6+-+10%2F6+
+t%5B3%5D+=+3%2F2+ hrs
--------------------
+d%5B1%5D+=+75%2At%5B1%5D+
+d%5B1%5D+=+75%2A%28+5%2F3+%29+
+d%5B1%5D+=+125+ mi
and
+d%5B2%5D+=+%28+280+-+40+%29%2At%5B2%5D+
+d%5B2%5D+=+%28+280+-+40+%29%2A2+
+d%5B2%5D+=+240%2A2+
+d%5B2%5D+=+480+ mi
-------------------
+d%5B1%5D+%2B+d%5B2%5D+=+125+%2B+480+
+d%5B1%5D+%2B+d%5B2%5D+=+605+
---------------------
Distance from A to C is 605 mi
----------------------------
check:
+d%5B2%5D+=+%28+280+%2B+40+%29%2At%5B3%5D+
+d%5B2%5D+=+%28+280+%2B+40+%29%2A%283%2F2%29+
+d%5B2%5D+=+320%2A%283%2F2%29+
+d%5B2%5D+=+480+ mi
OK