SOLUTION: After making a trip of 126 miles, a lady found that if she had increased her average speed by 8mph, she could have made the trip in 1 hour less time. Find her original speed.
My
Algebra ->
Customizable Word Problem Solvers
-> Travel
-> SOLUTION: After making a trip of 126 miles, a lady found that if she had increased her average speed by 8mph, she could have made the trip in 1 hour less time. Find her original speed.
My
Log On
Question 761850: After making a trip of 126 miles, a lady found that if she had increased her average speed by 8mph, she could have made the trip in 1 hour less time. Find her original speed.
My 2 equations:
original: 126=(s+8)*(t-1)
theoretical trip: 126=s*t
After I plug the 2nd equation into the first I do not know what to do.
126=(s+8)*((126/s)-1)
Please help! Thank You Thank You Thank You!!!!! -Abby Found 2 solutions by Alan3354, ankor@dixie-net.com:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! After making a trip of 126 miles, a lady found that if she had increased her average speed by 8mph, she could have made the trip in 1 hour less time. Find her original speed.
My 2 equations:
original: 126=(s+8)*(t-1)
theoretical trip: 126=s*t
After I plug the 2nd equation into the first I do not know what to do.
126=(s+8)*((126/s)-1)
------------
Solve for s
126 = (s+8)*((126-s/s))
126s = -s^2 + 118s + 1008
s^2 + 8s - 1008 = 0
(s+36)*(s-28) = 0
s = 28 mi/hr
--------------
126/28 = 4.5 hours
126/36 = 3.5 hours
You can put this solution on YOUR website! After making a trip of 126 miles, a lady found that if she had
increased her average speed by 8mph, she could have made the trip
in 1 hour less time.
Find her original speed.
:
Let's try it this way.
:
Let s = original speed
then
(s+8) = her increase speed
:
Write a time equation: time = dist/speed
:
Original time - faster speed time = 1 hr - = 1
multiply by s(s+8) cancel the denominators, resulting in
126(s+8) - 126s = s(s+8)
126s + 1008 - 126s = s^2 + 8s
combine all this, we have a quadratic equation of:
s^2 + 8s - 1008 = 0
Factors to
(s+36)(s-28) = 0
the positive solution is all we need here
s = 28 mph is the original speed
:
:
We can check this by finding the time at each speed
126/28 = 4.5 hrs
126/36 = 3.5 hrs (8mph faster)
-----------------
time dif: 1 hr
