SOLUTION: Wilma drove at an average speed of 40 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 35 mi/h. She returned

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Wilma drove at an average speed of 40 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 35 mi/h. She returned      Log On


   

Question 898420: Wilma drove at an average speed of 40 mi/h from her home in City A to visit her sister in City B. She stayed in City B 10 hours, and on the trip back averaged 35 mi/h. She returned home 40 hours after leaving. How many miles is City A from City B.
Other info:
The solution cannot be calculated using the formula that already exists to find distances using time and speed.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Wilma had +40+-+10+=+30+ actual
hours of driving time
Let +t+ = time in hrs for her to
drive from A to B
+30+-+t+ = time in hrs for her to
drive from B to A
Let +d+ = one-way distance from A to B
-------------------------------------
Equation for A to B:
+d+=+40t+
Equation for B to A
+d+=+35%2A%28+30+-+t+%29+
---------------------
By substitution:
+40t+=+35%2A%28+30+-+t+%29+
+40t+=+1050+-+35t+
+75t+=+1050+
+t+=+14+
and
+30+-+t+=+16+
-----------------
+d+=+40t+
+d+=+40%2A14+
+d+=+560+
-----------------
City A is 560 miles from City B
-----------------
check:
+d+=+35%2A%28+30+-+t+%29+
+560+=+35%2A%28+30+-+14+%29+
+560+=+35%2A16+
+560+=+560+
OK