Distance word problems: Marie rode her bicycle....

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leyton

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Aug 1, 2006
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1. Marie rode her bicycle from her home to the bicycle shope in town and
then walked back home. If she averaged 6 miles per hour riding and 3
miles per hour walking, how far is it from her home to the bicycle shop if
her total travel time was 1 hour?

i tried the chart.

Distance Rate Time
Biking d 6mph t
Walking d 3mph 1-t
Total t

I added those two distances together but did not come up with the answer which is 2. Help. If you could show me a formulaic step by step method of solving this problem this solution should show me how to solve other word problems.
 
1. Marie rode her bicycle from her home to the bicycle shope in town and
then walked back home. If she averaged 6 miles per hour riding and 3
miles per hour walking, how far is it from her home to the bicycle shop if
her total travel time was 1 hour?

i tried the chart.

Distance Rate Time
Biking d 6mph t
Walking d 3mph 1-t
Total t

I added those two distances together but did not come up with the answer which is 2. Help. If you could show me a formulaic step by step method of solving this problem this solution should show me how to solve other word problems.
Click to expand...
The total time T = D/6 + D/3 = 1

I'm certain you can take it from here.
 
Re: Distance word problems

leyton said:
Distance Rate Time
Biking d 6mph t
Walking d 3mph 1-t
Total t

I added those two distances together but did not come up with the answer which is 2.
Click to expand...
You ADDED? WHY?

distance = speed times time

Biking: d = 6t
Walking: d = 3(1 - t)
 
I came up with those figures and multiplied but still came up with the wrong answer.

Biking= 6t
walking=3(t-1)
 
First, the distance cannot be '2'. It needs units. Miles, maybe?

Distance = Rate * Time.

The distance is the same both ways. The total distance is 2*d.

The rate is given both ways. The average rate is what is asked in the problem statement.

The time is given ONLY in total.

(Total Distance) = (Average Rate) * (Total Time)

Please do not say you added or multiplied. Apply the formulas given. Stop guessing.
 
Okay I'll start from scratch.

Distance Rate Time
Biking D 6mph t
walking D 3mph t-1
Total --- ---- 1

1st row= 6t
2nd row= 3(t-1)=3t-3

how does this work out too be, excuse me, 2 miles.
 
The time it took to travel D miles at an average speed of 6mph is D/6 hours.
The time it took to travel D miles at an average speed of 3mph is D/3 hours.
The total time for the round trip is 1 hour.
Therefore, D/6 + D/3 = 1 or 9D/18 = 1 or 9D = 18 making D = 2 miles.
The bike trip took (D/6) = (2/6) = 1/3 hours = 20 minutes.
The walking trip took (D/3) = (2/3 = 2/3 hour = 40 min.
Total travel time = 20 min. + 40 min. = 1 hour.
 
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