SOLUTION: okay. So i'm very confused and stuck on this problem. i really need help. here is the question: Diana's average driving speed is 8 miles per hour faster than Damon's. In the

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: okay. So i'm very confused and stuck on this problem. i really need help. here is the question: Diana's average driving speed is 8 miles per hour faster than Damon's. In the       Log On


   

Question 248851: okay. So i'm very confused and stuck on this problem. i really need help. here is the question:
Diana's average driving speed is 8 miles per hour faster than Damon's. In the same lenth of time it takes Diana to drive 432 miles, Damon only drives 368 miles. for how long did diana and Damon each drive?
Please i need for someone to show the work and explain it to me so that i can understand it thank you!
Found 2 solutions by ankor@dixie-net.com, nerdybill:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Diana's average driving speed is 8 miles per hour faster than Damon's.
In the same length of time it takes Diana to drive 432 miles, Damon only drives 368 miles.
for how long did Diana and Damon each drive?
:
Let s = Damon's speed
then it says Diana's speed is 8 mph faster so we can say:
(s+8) = Diana's speed
:
We will find the speed first, then the time
The two trips took equal time so write a time equation: Time = dist/speed
:
Diana's time = Damon's time
432%2F%28%28s%2B8%29%29 = 368%2Fs
Cross multiply
432s = 368(s+8)
;
432s = 368s + 2944
:
432s - 368s = 2944
:
64s = 2944
s = 2944%2F64
s = 46 mph is Damon's speed
and
46 + 8 = 54 mph is Diana's speed
;
Find the time:
368/46 = 8 hrs
check to see they are equal
432/54 = 8 hrs also, confirms our solution
:
:
Did this unconfuse you somewhat?

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Diana's average driving speed is 8 miles per hour faster than Damon's. In the same lenth of time it takes Diana to drive 432 miles, Damon only drives 368 miles. for how long did diana and Damon each drive?
.
You need to apply the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let x = speed of Damon
then
x+8 = speed of Diana
.
Let t = time driven
then
tx = 368 (equation 1 -- Damon)
t(x+8) = 432 (equation 2 -- Diana)
.
Solve equation 1 for x:
tx = 368
x = 368/t
Substitute the above into equation 2:
t(x+8) = 432
t(368/t+8) = 432
368 + 8t = 432
8t = 64
t = 8 hours