SOLUTION: HELP, PLZ..... A woman commutes to work first by train, then rides a bicycle from the station to her office. The train averages 50 mi/h, and she averages 15 mi/h on her bicycle. T

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Question 436052: HELP, PLZ.....
A woman commutes to work first by train, then rides a bicycle from the station to her office. The train averages 50 mi/h, and she averages 15 mi/h on her bicycle. The total distance of her commute is 13 miles, and the combined trip takes 24 minutes. How far does she ride the train?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A woman commutes to work first by train, then rides a bicycle from the station to her office.
The train averages 50 mi/h, and she averages 15 mi/h on her bicycle.
The total distance of her commute is 13 miles, and the combined trip takes 24 minutes.
How far does she ride the train?
:
Let d = distance rode on the train
then
(13-d) = distance rode on the bike
:
Convert 24 min: 24/60 = .4 hrs
:
Write a time equation: Time = dist/speed
:
Train time + bike time = total time
+ = .4 hrs
Multiply by 150
150* + 150* = 150(.4)
cancel the denominators
3d + 10(13-d) = 60
3d + 130 - 10d = 60
3d - 10d = 60 - 130
-7d = -70
d = +10 miles on the train
:
:
Check by finding time of each
10/50 = .2 hr
3/15 = .2 hrs
--------------
total .4 hrs which is 24 min

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = her time spent on the train
Let = the distance she travels on the train
Equation for train:

Equation for bike:

By substitution:

Now find

She rides the train for 10 miles
check answer: