SOLUTION: 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 go

Algebra ->  Expressions-with-variables -> SOLUTION: 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 go      Log On


   

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

Answer by ankor@dixie-net.com(22740) 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%2F5 + %28%2893-d%29%29%2F13 = 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%2F8
d = 15 miles walked
the
15%2F5 = 3 hrs walking
:
Check solution, find the distance riding:
%2893-15%29%2F13 = 6 hr
so we have: 3 + 6 hrs = 9 hrs