# Math

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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 -

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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