Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.
Answer:
Dale live 315 miles from the mountains
Step-by-step explanation:
Let y be the speed of Dale to the mountains
Time taken by Dale to the mountains=7 hrs
Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1
Time taken by Dale back home = 5hours
Since it speed increased by 18 miles per hour back home it speed = y+18
So distance traveled home =speed × time = (y+18)5 ...... eqn 2
Since distance cover is same in both the eqn 1 and eqn 2.
Eqn 1 = eqn 2
7y = (y+18)5
7y = 5y + 90
7y - 5y = 90 (collection like terms)
2y = 90
Y = 45
Substitute for y in eqn 1 to get distance away from mountain
= 7y eqn 1
= 7×45
= 315 miles.
∴ Dale leave 315 miles from the mountains
We let x and y be the measures of the sides of the
rectangular garden. The perimeter subtracted with the other side should be
equal to 92.
<span> 2x + y = 92</span>
The value of y in terms of x is equal to,
<span> y =
92 – 2x</span>
The area is the product of the two sides,
<span>
A
= xy</span>
Substituting,
<span> A
= x (92 – 2x) = 92x – 2x2</span>
Solving for the derivative and equating to zero,
<span> 0
= 92 – 4x ; x = 23</span>
Therefore, the area of the garden is,
<span> A
= 23(92 – 2(23)) = 1058 yard<span>2</span></span>
Answer:
Please check the attached file.
Hope this helps!
:)
Answer:
The answer is 6x -7y = 21
Step-by-step explanation:
Im taking the diagnostic
