Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

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Question 170453This question is from textbook Introductory Algebra
: Solve the problem. Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. How many hours did she walk?This question is from textbook Introductory Algebra
: Solve the problem. Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. How many hours did she walk?
Answer by ankor@dixie-net.com(4667) About Me  (Show Source):
You can put this solution on YOUR website!
Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph.
She traveled a total of 93 miles. Had she biked the whole time, she would have
gone 117 miles.
:
How many hours did she walk?
:
We know that if she biked the whole way, travel time would be: 117/13 = 9 hrs
:
This is also the travel time of walking and riding a total of 93 mi, implied by
the phrase."Had she biked the whole time"
:
Find the distance she walked, first.
Let d = distance walked
Then
(93-d) = distance she rode
:
Write a time equation: Time = dist/speed:
:
walking time + riding time = 9 hrs
d/5 + ((93-d))/13 = 9
:
Multiply equation by 65 to get rid of the denominators, results:
13d + 5(93-d) = 65(9)
:
13d + 465 - 5d = 585
:
13d - 5d = 585 - 465
:
8d = 120
d = 120/8
d = 15 miles walked
the
15/5 = 3 hrs walking
:
Check solution, find the distance riding:
(93-15)/13 = 6 hr
so we have: 3 + 6 hrs = 9 hrs