SOLUTION: A cross country skier walks 3000m up a mountain road, rests for 10 minutes and then skis down the road. he returns a half hour after he started. if he skis four times as fast as he

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Question 279459: A cross country skier walks 3000m up a mountain road, rests for 10 minutes and then skis down the road. he returns a half hour after he started. if he skis four times as fast as he walks, at what rate does he ski?
( having a hard time grasping these word problems and what dictates a constant factor and how to build the equation.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A cross country skier walks 3000m up a mountain road, rests for 10 minutes
and then skis down the road.
he returns a half hour after he started. if he skis four times as fast as
he walks, at what rate does he ski?
:
Change half hour to 30 min
:
Let w = his walking speed (in meters/minute)
then
4w = his skiing speed
:
Write a time equation: time = dist/speed
:
up time + 10 min + down time = 30 min
+ 10 + = 30
Multiply by 4W,results
4(3000) + 4w(10) + 3000 = 4w(30)
:
12000 + 40w + 3000 = 120w
:
12000 + 3000 = 120w - 40w
:
15000 = 80w
w =
w = 187.5 m/min; his walking speed
and
4(187.5) = 750 m/min is his skiing speed
:
That would be: = 45 km/hr
:
:
Check solution by finding the times
3000/187.5 = 16 min
resting time:10 min
3000/750.0 = 4 min
---------------------
total time = 30 min; confirms our solution