SOLUTION: Mark walked for 60 minutes and biked for 90 minutes. He bikes four times faster than he walks. If the total distance traveled is 14 miles, then what was his biking speed in MPH?

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Question 179360This question is from textbook intermediate algebra
: Mark walked for 60 minutes and biked for 90 minutes. He bikes four times faster than he walks. If the total distance traveled is 14 miles, then what was his biking speed in MPH? This question is from textbook intermediate algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can write 2 equations, 1 for biking
and 1 for walking
(1) d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
(2) d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
------
Given:
t%5Bb%5D+=+90%2F60hrs
t%5Bw%5D+=+60%2F60hrs
r%5Bb%5D+=+4r%5Bw%5D
d%5Bb%5D+%2B+d%5Bw%5D+=+14mi
d%5Bb%5D+=+14+-+d%5Bw%5D
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Now I can rewrite (1) and (2)
(1) 14+-+d%5Bw%5D+=+4r%5Bw%5D%2A%2890%2F60%29
(2) d%5Bw%5D+=+r%5Bw%5D%2A%2860%2F60%29
-------
(1) -+d%5Bw%5D+=+4r%5Bw%5D%2A%283%2F2%29+-+14%29
(1) -d%5Bw%5D+=+6r%5Bw%5D+-+14
(2) d%5Bw%5D+=+r%5Bw%5D%2A%2860%2F60%29
(2) d%5Bw%5D+=+r%5Bw%5D
-------
Add (1) and (2)
0+=+6r%5Bw%5D+%2B+r%5Bw%5D+-+14
7r%5Bw%5D+=+14
r%5Bw%5D+=+2mi/hr
And, since
r%5Bb%5D+=+4r%5Bw%5D
r%5Bb%5D+=+4%2A2
r%5Bb%5D+=+8mi/hr
His biking speed was 8 mi/hr
check:
-d%5Bw%5D+=+6r%5Bw%5D+-+14
-d%5Bw%5D+=+6%2A2+-+14
-d%5Bw%5D+=+-2
d%5Bw%5D+=+2mi
And
d%5Bb%5D+=+14+-+d%5Bw%5D
d%5Bb%5D+=+14+-+2
d%5Bb%5D+=+12mi
(1) d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
12+=+8%2A%283%2F2%29
12+=+12
OK
(2) d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
2+=+2%2A1
2+=+2
OK