Question 1105157: An avalanche rescue team travels 8.55 km along a snow-covered trail. For the first section, the trail is flat. The team averages a speed of 2.7 km/h. Then, the terrain becomes mountainous and their average speed is only 1.2 km/h. The one-way trip takes the team 4.0 h. Determine the distance that the team travels on each type of terrain
Answer by stanbon(75887)   (Show Source):
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An avalanche rescue team travels 8.55 km along a snow-covered trail. For the first section, the trail is flat. The team averages a speed of 2.7 km/h. Then, the terrain becomes mountainous and their average speed is only 1.2 km/h. The one-way trip takes the team 4.0 h. Determine the distance that the team travels on each type of terrain
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Equations::
Distance Equation:: f + s = 8.55 km
Time Equation:::::f/2.7 + s/1.2 = 4 hrs
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Modify the Time equation::
1.2f + 2.7s = 1.2*2.7*4
12f + 27s = 12*2.7*4
12f + 27s = 129.6
Modify the Distance equation::
12f + 12s = 12*8.55
Subtract and solve for "s":
15s = 27
s = 9/5 = 1 4/5 km (mountainous leg distance)
8.55-1.8 = 7.75 = 7 3/4 km (flat leg distance)
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Cheers,
Stan H.
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