SOLUTION: You drive 90 miles to a hiking trail, and then take a 5 mile hike. The driving time is 9x that of your walking time. The total time for driving and hiking is 3 hours, find the av

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: You drive 90 miles to a hiking trail, and then take a 5 mile hike. The driving time is 9x that of your walking time. The total time for driving and hiking is 3 hours, find the av      Log On

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Question 327378: You drive 90 miles to a hiking trail, and then take a 5 mile hike. The driving time is 9x that of your walking time. The total time for driving and hiking is 3 hours, find the average rate of driving and the average rate of hiking.

Found 2 solutions by Fombitz, NathanC:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
.
Let D be the driving rate, W the walking rate,
D%2A%289t%29=90
1.D%2At=10
2.W%2At=5
.
.
t%2B9t=3
10t=3
3.t=0.3
From eq. 1,
D=10%2F0.3=33.3mph
From eq. 2,
W=5%2F0.3=16.7 mph
That's a pretty fast walking rate.

Answer by NathanC(1) About Me  (Show Source):
You can put this solution on YOUR website!
3 = 5/x + 90/9x
LCD = 9x
Restriction: x ≠ 0

27x = 45 + 90
27x = 135
x = 5

The walking rate is 5 MPH and the driving rate is 45 MPH.