SOLUTION: Connie walks from her home to the bicycle repair shop at 6 km/h and then bikes home at 20 km/h. If the total traveling time is 39 minutes, how far is it from her home to the repair

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Question 1208126: Connie walks from her home to the bicycle repair shop at 6 km/h and then bikes home at 20 km/h. If the total traveling time is 39 minutes, how far is it from her home to the repair shop?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) (Show Source):
You can put this solution on YOUR website!

SPEED TIME DISTANCE in kilometers WALK 6 d BIKE 20 d Total

d, the unknown distance each way
Total time as hours, is , and seems more convenient not to reduce this.

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(Yes, you can do this all in symbols if you want to.)

Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

The other tutor shows the setup for a typical formal algebraic solution.

Here is a very different way to set up and solve the problem -- which I personally find much easier and faster than the formal algebraic method.

The distances to and from the repair shop are the same; therefore, since the ratio of speeds is 6:20 = 3:10, the ratio of times at the two speeds is 10:3.

Let 10x = time (minutes) at 6mph
let 3x = time at 20mph
The total time is 39 minutes:
10x+3x = 39
13x = 39
x=3
10x = 30 = time at 6mph
3x = 9 = time at 20mph

(or perhaps you can do the preceding calculation mentally -- 39 minutes in the ratio 10:3 means 30 minutes and 9 minutes....)

She spent 30 minutes = 1/2 hour walking to the repair shop at 6mph. So the distance from her home to the repair shop is 6(1/2) = 3 miles.

ANSWER: 3 miles