SOLUTION: Jill walked at a constant rate for 2 hours and then ran twice that rate for 1/2 an hour. She traveled 18 km in all. What was her walking rate?

Question 8621: Jill walked at a constant rate for 2 hours and then ran twice that rate for 1/2 an hour. She traveled 18 km in all. What was her walking rate?
Answer by glabow(165) (Show Source): You can put this solution on YOUR website!
This can be solved intuitively. If you go 10 km/hr for an hour you travel 10 km, right? So if you go twice as fast for half as long, don't you travel the same as the old rate for twice as long? That is rate x time = distance. 2 x rate x time / 2 = distance. The distance is the same.
So, this problem is really rate x 2 hours + rate x one hour, or rate x 3 hours.
Well, that's 18 km in 3 hours. What's the rate per hour? [If you said 6 km/hr, you are right!]
However, doing this algebraically would be prudent, since the factors involved are not always so even.
Let r be the rate at which she walks.
She traveled 2 hours times r km/hour in the first 2 hours.
She traveled .5 hours times 2r in the next 1/2 hour.
.5 x (2r) + 2 x (r) = 18 km.
This comes out to be r + 2r = 18, or 3r = 18. We are not surprised.
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