Question 65498This question is from textbook Essential Algebra
: Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph fater than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike?
This question is from textbook Essential Algebra
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph faster than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike?
The formula for distance is:  , where d=distance, r=rate(or speed), and t=time
Givens for the hike protion:
t=4
r=r (we don't know it)
d=4r
Givens for the bike protion:
t=8
r=r+10 (10 mph faster than they can hike.)
d=8(r+10)
The total of the trip= 122
Problem to solve:
4r+8(r+10)=122
4r+8r+80=122
12r+80=122
12r+80-80=122-80
12r=42
12r/12=42/12
r=3.5
Therefore the rate that they can bike: r+10=3.5+10=13.5 mph
:
Sanity check:
If they hiked for 4 hrs at 3.5 mph and biked for 8 hrs at 13.5 mph, would they travel 122 mi?
4(3.5)+8(13.5)=122 ?
14+108=122
122=122 It appears we are sane.
Happy Calculating!!!!
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website! Abigail Nightwind has planned a bike trip with
some friends from her village. They will bike
for 8 hours, then hike for 4 hours. If they
can bike on the average 10mph fater than they
can hike and if they will cover a total of 122
miles, how fast can Abigail and her friends
bike?
Funmath above let the unknown represent
the hiking rate. To be a little different,
I'm going to let the unknown represent the
biking rate instead. After all that's what
we're asked for in the question. I also
think it makes it easier to see if you use
a DRT chart.
Let x = the biking rate.
Make this DRT-chart
D R T
biking
hiking
and fill in x for the biking rate:
D R T
biking x
hiking
>>...They can bike on the average 10mph faster
than they can hike...<<
This means that they can hike on the average
10mph slower than they can bike. So their hiking
rate is 10mph slower or x-10. So fill that in
for the hiking rate
D R T
biking x
hiking x-10
>>..They will bike for 8 hours, then hike for
4 hours...<<
So fill in 8 for the biking time, and 4 for
the hiking time:
D R T
biking x 8
hiking x-10 4
Now we fill in the distances using D = RT
D R T
biking 8x x 8
hiking 4(x-10) x-10 4
Now that the chart is filled in, we return
to the word problem to see what we have not
used in filling in the chart. It is these
words:
>>...They will cover a total of 122 miles...<<
So,
distance biking + distance hiking = 122 miles
8x + 4(x-10) = 122
8x + 4x - 40 = 122
12x - 40 = 122
12x = 162
x = 162/12
x = 27/2
x = 13.5 mph
Checking: They bike at 13.5mph and hike at 3.5mph
They bike at 13.5mph for 8 hours and that's a distance
of 108 miles they bike.
They hike at 3.5mph for 4 hours and that's a distance
of 14 miles they hike.
108 miles biked + 14 miles hiked = 122 miles total.
Edwin
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