Question 475392: David and Keith are route drivers for a fast-photo company. David's route is 80 miles, and keith's is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minutes before David. What is David's speed?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Dave travels 80 miles.
Keith travels 100 miles.
Dave's speed is x miles per hour.
Keith's speed is x+10 miles per hour.
Dave's Time is equal to T hours.
Keith's Time is equal to T - 1/6 hours which is equivalent to (6T-1)/6 hours.
rate * time = distance.
For Dave, this becomes:
x * T = 80
For Keith, this becomes:
(x+10)*(6T-1)/6 = 100
Solve these 2 equations simultaneously and you have the answer to your problem.
The 2 equations you need to solve simultaneously are:
x * T = 80
(x + 10) * ((6T-1)/6) = 100
If you solve for x in the first equation, you get:
x = 80/T
substituting in the second equation, you get:
(80/T + 10) * ((6T-1)/6) = 100
multiply both sides of this equation by 6 and you get:
(80/T + 10) * (6T-1) = 600
multiply both sides of this equation by T and you get:
(80 + 10T) * (6T-1) = 600T
Multiply the factors out and you get:
-10T - 80 + 60T^2 + 480T = 600T
combine like terms and you get:
470T - 80 + 60T^2 = 600T
subtract 600T from both sides of this equation and you get:
-130T - 80 + 60T^2 = 0
reorder the terms of this equation and you get a quadratic equation of:
60T^2 - 130T - 80 = 0
divide both sides of this equation by 10 and you get:
6T^2 - 13T - 8 = 0
This equation factors out to be:
(3T - 8) * (2T + 1) = 0
This gets you:
3T = 8 or 2T = -1
Since T can't be negative, the only possible answer would be 3T = 8
This results in T = 8/3
If T = 8/3, then x*T = 80 results in x = 80/T which results in x = 80/(8/3) which results in x = 80 * (3/8) which results in x = 240/8 which results in x = 30.
You now have:
x = 30 miles per hour.
T = 8/3 hours.
If x = 30, then (x+10) = 40
If T = 8/3, then T-(1/6) = 15/6
We can now substitute for Dave and Keith's equations to see if the values of x and T are good.
For Dave:
x * T = 80 results in 30 * 8/3 = 80 which is good.
For Keith:
(x+10) * (T-1/6) results in 40 * 15/6 = 100 which is also good.
The answer to your question is:
Dave's speed is 30 miles per hour.
|
|
|
