Question 1058835: you drive 28 miles to a friend's house and it takes you 1.26 hours to get there. Suppose that your speed during the second 14 miles was 5 MPH faster than your speed during the first 14 miles. What was your speed during the first 14 miles?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
speed time distance
FIRST r 14
SECND r+5 14
Total 1.26 28
Constant Travel Rates Rule for RATE R, TIME T, DISTANCE D, is
RT=D.
Do you see what to do?
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! i believe the answer will be that you drove at 20 miles per hour for 14 miles and you drove at 25 miles per hour for 14 miles.
your speed during the first 14 miles was 20 miles per hour.
that would be your solution.
here's how i derived that.
you are given that the total time took 1.26 hours.
if you let x = the time for the first 14 miles, the 1.26 - x equals the time for the second 14 miles.
if you let y equal the rate you traveled at for the first 14 miles, then y + 5 equals the rate you traveled at for the second 14 miles.
since rate * time = distance, your formulas become:
x * y = 14 for the first 14 miles.
(1.26 - x) * (y + 5) = 14 for the second 4 miles.
solve for y in the first formula to get y = 14/x.
replace y with 14/x in the second formula to get:
(1.26 - x) * (14/x + 5) = 14
distribute the multiplication to get:
1.26 * 14/x + 5*1.26 - x*14/x - 5x = 14
simplify to get:
17.65/x + 6.3 - 14 - 5x = 14
multiply both sides of the equation by x to get:
17.65 + 6.3x - 14x - 5x^2 = 14x
subtract 14x from both sides of the equation to get:
17.65 + 6.3x - 14x - 5x^2 - 14x = 0
combine like terms to get:
17.65 - 21.7x - 5x^2 = 0
reorder the terms in descending order of degree to get:
-5x^2 - 21.7x + 17.65 = 0
solve using the quadratic formula to get:
x = -5.04 or x = .7
x can't be negative, so x is equal to .7
x represents time.
1.26 - x = 1.26 - .7 = .56
it took him .7 hours to travel the first 14 miles.
it took him .56 hours to travel the second 4 miles.
since rate * time = distance, and since x = time and y = rate, you get:
y * .7 = 14
solve for y to get y = 14/.7 = 20 miles per hour.
this makes y + 5 = 25 miles per hour.
he traveled at 20 miles per hour for the first 14 miles and 25 miles per hour for the second 14 miles.
the total time it took was .7 hours for the first 14 miles and .56 hours for the second 14 miles for a total of 1.26 hours.
|
|
|
