SOLUTION: Simon and Jane leave the train station at the same time. Simon is jogging east at 5 miles per hour. Jane is riding her bike west at 10 miles per hour. A. How far apart will they b

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Simon and Jane leave the train station at the same time. Simon is jogging east at 5 miles per hour. Jane is riding her bike west at 10 miles per hour. A. How far apart will they b      Log On


   



Question 1147058: Simon and Jane leave the train station at the same time. Simon is jogging east at 5 miles per hour. Jane is riding her bike west at 10 miles per hour.
A. How far apart will they be after 2.5 hours?
B. How long will it take them to be 25 miles apart?

Found 2 solutions by greenestamps, josmiceli:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


They are separating at a rate of 5+10=15mph.

A. 15 miles per hour times 2.5 hours: 2.5 * 15

B. 25 miles divided by 15 miles per hour: 25/15

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since they are moving apart, their speeds will add.
You can think of one of them standing still and the
other one moving at the sum of their speeds
-------------------------------------------------
A.
Let +d+ = their distance apart after +2.5+ hrs
+d+=+%28+10+%2B+5+%29%2A2.5+
+d+=+15%2A2.5+
+d+=+37.5+ mi
--------------------------
B.
Let +t+ = time in hrs for them to be +25+ mi apart
+25+=+%28+10+%2B+5+%29%2At+
+25+=+15t+
+t+=+1.667+ hrs
1 hr 40 min
====================
check answers:
A.
Simon's equation:
+d%5B1%5D+=+5%2A2.5+
+d%5B1%5D+=+12.5+ mi
and
Jane's equation:
+d%5B2%5D+=+10%2A2.5+
+d%5B2%5D+=+25+ mi
and
+d%5B1%5D+%2B+d%5B2%5D+=+12.5+%2B+25+
+d+=+37.5+
OK
----------------
B.
Simon's equation:
+d%5B1%5D+=+5t+
and
Jane's equation:
+d%5B2%5D+=+10t+
+d%5B1%5D+%2B+d%5B2%5D+=+5t+%2B+10t+
+25+=+15t+
+t+=+1.667+ hrs
OK