Mathematics, 20.09.2020 14:01 davidb1113

On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph on the highway and 40 mph through cities, he can only go 20 mph past the construction. He spends one half the time on the highway as he does in construction, so the 380-mile trip takes 11 hours. How much of this time does he spend on the highway, in the city, and through road construction?

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Answer from: naynay4evr

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway d_1 = 60 mph

Let the time taken to travel on highway = t_1 hours

Distance traveled = 60t_1 miles

Speed in the city = 40 mph

Let the time taken = t_2 hours

Distance traveled in the city = 40t_2 miles

Speed on the construction = 20 mph

Let the time spend on the construction = t_3 hours

Distance traveled on the construction = 20t_3 miles

Since, total distance covered = 380 miles

d_1+d_2+d_3=60t_1+40t_2+20t_3

He spends one half the time on the highway as he does on the construction,

t_3=2t_1

Total time spent in the trip = 11 hours

Therefore, t_1+t_2+t_3=11

t_1+t_2+2t_1=11

t_2=11-3t_1

From equation (1),

60t_1+40(11-3t_1)+20(2t_1)=380

60t_1-120t_1+40t_1+440=380

440-20t_1=380

20t_1=440-380

$t_1=\frac{60}{20}$

t_1=3 hours

t_2=11-3t_1=2 hours

t_3=2t_1=6 hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

what is the graph

step-by-step explanation:

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On a trip, Duke encounters some road construction that slows him down. While he is able to go 60 mph...