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.
Greater. This is because 1/2 x 10/10 = 10/20. 11>10
Answer: See explanation
Step-by-step explanation:
Total water fetched = 24 pints.
Jill drank a tenth of this. This will be:
= 1/10 × 24
= 2.4 pints
Jack drank a quarter. This will be:
= 1/4 × 24 = 6.
They gave three eighths to dame Dob . Thus will be:
= 3/8 × 24
= 9
They gave a fifth to jill's mother. This will be:
= 1/5 × 24.
= 4.80
Amount that'll be left over will be:
= 24 - (2.40 + 6 + 9 + 4.80)
= 24 - 22.2
= 1.8
1.8 pints of water will be left over.
