Posted by Sioux on Thursday, June 18, 2009 at 8:56am.
The road connecting two mountain villages goes only uphill or downhill. A bus always travels 15 mph uphill and 30 mph downhill. Find the distance between the villages if it takes exactly four hours for the bus to complete a round trip.

Math  Reiny, Thursday, June 18, 2009 at 9:13am
I always had my students do these questions by organizing the information in a chart.
let the time take to go uphill be t hours
then the time taken to go downhill is 4t hours
.......... Dist.....rate..time
uphill: ....15t......15....t
downhill....30(4t) ..30...4t
(I hope this somehow lined up)
but the distance is the same, so
15t = 30(4t)
15t = 120  30t
45t = 120
t = 8/3
distance = 15t = 15(8/3)
= 40 km