SOLUTION: Sharon Kobrin commutes to her office by train.When she walks to the train station,it takes her 40 min.When she rides her bike,it takes her 12 min.Her average walking rate is 7 mph

Algebra ->  Finance -> SOLUTION: Sharon Kobrin commutes to her office by train.When she walks to the train station,it takes her 40 min.When she rides her bike,it takes her 12 min.Her average walking rate is 7 mph       Log On


   

Question 1016904: Sharon Kobrin commutes to her office by train.When she walks to the train station,it takes her 40 min.When she rides her bike,it takes her 12 min.Her average walking rate is 7 mph less than her average biking rate.Find the distance from her house to the train station.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert all minutes to hours
+40%2F60+=+2%2F3+ hrs
+12%2F60+=+1%2F5+ hrs
Let +r+ = her average biking rate
Let +d+ = distance in miles to train station
-------------------------------------
Equation for walking:
(1) +d+=+%28+r-7+%29%2A%282%2F3%29+
Equation for biking:
(2) +d+=+r%2A%281%2F5%29+
---------------------
+%28+r-7+%29%2A%282%2F3%29+=+r%2A%281%2F5%29+
Multiply both sides by +15+
++10%2A%28+r+-+7+%29+=+3r+
+10r+-+70+=+3r+
+7r+=+70+
+r+=+10+
and
+r+-+7+=+3+
---------------
(2) +d+=+r%2A%281%2F5%29+
(2) +d+=10%2A%281%2F5%29+
(2) +d+=+2+
and
(1) +d+=+%28+r-7+%29%2A%282%2F3%29+
(1) +d+=3%2A%282%2F3%29+
(1) +d+=+2+
The distance to the train station is 2 mi