Answer: Downhill:10mph Uphill:5mph
Step-by-step explanation:
We are looking for Dennis’s downhill speed.
Let
r=
Dennis’s downhill speed.
His uphill speed is
5
miles per hour slower.
Let
r−5=
Dennis’s uphill speed.
Enter the rates into the chart. The distance is the same in both directions,
20
miles.
Since
D=rt
, we solve for
t
and get
t=
D
r
.
We divide the distance by the rate in each row and place the expression in the time column.
Rate
×
Time
=
Distance
Downhill
r
20
r
20
Uphill
r−5
20
r−5
20
Write a word sentence about the time.
The total time traveled was
6
hours.
Translate the sentence to get the equation.
20
r
+
20
r−5
=6
Solve.
20(r−5)+20(r)
40r−100
0
0
0
=
=
=
=
=
6(r)(r−5)
6
r
2
−30r
6
r
2
−70r+100
2(3
r
2
−35r+50)
2(3r−5)(r−10)
Use the Zero Product Property.
(r−10)=0
r=10
(3r−5)=0
r=
5
3
The solution
5
3
is unreasonable because
5
3
−5=−
10
3
and his uphill speed cannot be negative. So, Dennis's downhill speed is
10
mph and his uphill speed is
10−5=5
mph.
Check. Is
10
mph a reasonable speed for biking downhill? Yes.
Downhill:
10 mph
5 mph⋅
20 miles
5 mph
=20 miles
Uphill:
10−5=5 mph
(10−5) mph⋅
20 miles
10−5 mph
=20 miles
The total time traveled was
6
hours.
Dennis’ downhill speed was
10
mph and his uphill speed was
5
mph.
The empty jug weighs 0.75 lb
With the 3c, the total weighs 2.25 lb. That means:
3c + empty jug = 3c + 0.75 = 2.25
3c = 2.25 - 0.75
3c = 1.5
and 1c = 0.5 (so c is a constant -or the slope-)
Then the equation is:
y = 0.5x + 0.75
Answer:
9
Step-by-step explanation:
First, find <em>x</em>. Since <em>x</em> is the average of the three number, add the three up and then divided by three. Thus:
<em>y</em> is the cube root of 8. Thus:
![y=\sqrt[3]{8}=2](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7B8%7D%3D2)
So:
Just set it equal to zero and solve using the quadratic equation.
Answer:
6
Step-by-step explanation:
