Question 271451: During the day a truck driver encounters light ,moderate, & heavy traffic. If he travels 1/3 hour in light, 1/2 hour in moderate, and 1/5 hour in heavy he can cover 21 miles. Ifh e travels 1/5 in light, 1/4 in moderate, and 1 hr in heavy he can cover 16 mi. The sum of his speeds in moderate & heavy is 5 mi less than his speed in light. Find his speed in each type of traffic.
Use 3 variable system to solve.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! During the day a truck driver encounters light ,moderate, & heavy traffic.
If he travels 1/3 hour in light, 1/2 hour in moderate, and 1/5 hour in heavy he can cover 21 miles.
If he travels 1/5 in light, 1/4 in moderate, and 1 hr in heavy he can cover 16 mi.
The sum of his speeds in moderate & heavy is 5 mi less than his speed in light.
Find his speed in each type of traffic. :
:
Three different speed, fast, medium, slow: a, b, c
:
A first distance equation
 a +  b +  c = 21
Multiply by 30 to get rid of the fractions, results:
10a + 15b + 6c = 30(21)
10a + 15b + 6c = 630
:
2nd distance equation
a +  b + c = 16
Multiply by 20 to get rid of the fractions, results:
4a + 5b + 20c = 20(16)
4a + 5b + 20c = 320
:
"The sum of his speeds in moderate & heavy is 5 mi less than his speed in light."
b + c = a - 5
-a + b + c = -5
:
Using the matrix feature in a Ti83,
10, 15, 6, 630
4, 5, 20, 320
-1,1, 1, -5
I got
a = 30 mph
b = 20
c = 5
|
|
|
