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 4-t hours

.......... Dist.....rate..time

uphill: ....15t......15....t

downhill....30(4-t) ..30...4-t

(I hope this somehow lined up)

but the distance is the same, so

15t = 30(4-t)

15t = 120 - 30t

45t = 120

t = 8/3

distance = 15t = 15(8/3)

= 40 km

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