Respuesta :
Answer:
The answer to the question is
36 mph on her way home and 45 mph on her way to visit her parents
Step-by-step explanation:
Total time for driving = 24 hours
Distance covered = 480 miles × 2
Speed of Jessie on her way home = x mph
Speed of Jessie on her way to visit her parents = x+9 mph
Therefore since speed = distance/time then we have
480/x + 480/(x+9) = 24
which gives [tex]\frac{960x+4320}{x(x+9)} = 24[/tex] we cross multply and we have
24x²-744x-4320 = 0 which gives
(x+5)(x-36)×24 = 0 This means that her speed on her way home is either -5 mph (which is in reverse direction) or or 36 mph
Therefore her speed is 36 mph on her way home and 36+9 or 45 mph on her way to her parents
Answer: Jessie's speed while going to her parents' residence was 44.99 miles per hour and her speed as she returned was 36.01 miles per hour
Step-by-step explanation:
Let us use 'b' to denote the number of hours she spent en route to her parents' residence and use 'c' to denote the number of hours she spent on her way home.
If the parents live 480 miles away, then her speed going there should be 480/b mph (speed = distance/time taken)
Jessie's speed while returning home from her parents' residence should be 480/c mph.
Recall that her average speed while going was 9mph faster than her average speed while returning.
That means (480/b) mph - (480/c) mph = 9mph.
Also, she spent a total of 24 hours going and returning.
This implies that b hours + c hours = 24 hours. Now we have two equations:
480/b - 480/c = 9 ----- equation 1
b + c = 24 ------ equation 2
From equation 2, b = 24 - c (making b the subject of the formula). Then substitute b for 24 - c in equation 1
480/(24 - c) - 480/c = 9
Joining the first 2 fractions to have a common denominator, we have:
(960c - 11520)/(24c - c^2) = 9
Cross multiplying, we have 960c - 11520 = 216c - 9c^2
Gathering all the terms on a side, we have:
9c^2 + 744c - 11520
We now solve the quadratic equation before us to find c (note : c is the number of hours she spent returning home)
-744 + √[(744^2) - (4×9 × (-11520)]
--------------------------------------
2 × 9
= -744 + 984
------------------
18
= 240/18 = 13.33 hrs.
Therefore, c =13.33hrs.
She spent 13.33 hrs returning but b + c = 24
i.e b + 13.33 = 24
b = 24 - 13.33 = 10.67 hrs
This implies that she spent only 10.67 hrs on her way to her parents' residence.
Since speed = distance/time, her speed going there = 480/10.67 = 44.99 mph(rounding to 2 decimal places)
While her speed returning = 480/13.33 = 36.01 mph (rounding to 2 decimal places)
