SOLUTION: The traveling time is 25 minutes shorter if you higher the average speed by 5 km/hour. Raising the average speed by another 5 km/hour lowers the traveling time by another 20 mi

Click here to see ALL problems on Travel Word Problems

Question 637342: The traveling time is 25 minutes shorter if you higher the average speed by 5
km/hour. Raising the average speed by another 5 km/hour lowers the traveling
time by another 20 minutes. What is the distance of the trail?
Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website!
Let trail length = Y
Let average speed = X
Let traveling time = T
We have three unknowns so you need three equations:
Equation 1: T = Y/X
Equation 2: T - 25 = Y /(X+5)
Equation 3: T - 25 - 20 = Y / (X + 5 + 5)
Rewrite equation 3
T - 45 = Y / (X + 10)
----------------------------
Solve equation 1 for Y
Equation 1: T = Y/X
Multiply both sides by X
T*X = Y
Substitute T*X into equation 3 for Y
T - 45 = Y / (X + 10)
T - 45 = T*X / (X + 10)
Multiply both sides by (X + 10)
(X + 10)* (T - 45) = T*X
Simplify
T*X - 45X + 10T - 450 = T*X
Subtract T*X from both sides.
-45X + 10T - 450 = 0
Add 45X & 450 to both sides
10T = 45X + 450
Divide both sides by 10
T = 4.5X + 45
----------------------------
Now Plug T*X into equation 2 for Y, and use (4.5X + 45) for T
Equation 2: T - 25 = Y /(X+5)
T - 25 = T*X / (X+5)
4.5X + 45 - 25 = ((4.5X + 45)*X) / (X + 5)
Simplify
4.5X + 20 = (4.5X^2 + 45X) / (X+5)
Multiply both sides by (X+5)
(X+5) * (4.5X + 20) = 4.5X^2 + 45X
Simplify
4.5X^2 + 20X + 22.5X + 100 = 4.5X^2 + 45X
Subtract 4.5X^2 from both sides
20X + 22.5X + 100 = 45X
Combine like terms
42.5X + 100 = 45X
Subtract 42.5X from both sides
100 = 2.5X
Divide both sides by 2.5

--------------------------------
Earlier we stated that T = 4.5X + 45.
Plug 40 in for X and solve for T
T = 4.5*(40) + 45
T = 180 + 45

--------------------------------
Now plug 40 into equation 1 for X and use 225 for T.
Equation 1: T = Y/X
225 = Y/40
Multiply both sides by 40

The trail is 9000km