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

#### leyton

##### New member
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.

#### TchrWill

##### Full Member
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.
The total time T = D/6 + D/3 = 1

I'm certain you can take it from here.

#### Denis

##### Senior Member
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.

distance = speed times time

Biking: d = 6t
Walking: d = 3(1 - t)

#### leyton

##### New member
I came up with those figures and multiplied but still came up with the wrong answer.

Biking= 6t
walking=3(t-1)

#### tkhunny

##### Moderator
Staff member
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.

#### leyton

##### New member
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.

#### TchrWill

##### Full Member
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.

thank you.