HELP ME The distance between two cities A and B is 140 km. A car driving from A to B left at the same time as a car driving from B to A. The cars met after one hour, then the first car reached city B 35 minutes later than the second car reached city A. Find the speed of the car from city A to B. *
A. 60 km/h
B. 50 km/h
C. 80 km/h
D. 70 km/h

The correct option is;

B. 50 km/h

Step-by-step explanation:

The information given in the question are;

The distance between the two cities = 140 km

The direction of motion of the first car = From A to B (left)

The direction of motion of the second car = From B to A

The time after which both cars meet = 1 hour

The time duration it takes after both cars meet for the second car to reach A = 35 minutes

The total time taken by the second car from city B to city A = The time it takes to meet the first car + The time it takes after meeting the first car to reach city A

∴ The total time taken by the second car from city B to city A = 1 hour + 35 minutes = 60 minutes + 35 minutes = 95 minutes

95 minutes = 95/60 hours = 1⁷/₁₂ hours =  1.58 hours

The speed of the second car = Distance/Time = 140 km/(1.58 hours) ≈ 88.42 km/h

Therefore, let the distance from A of the point the first car meet the second car = x

Therefore, we have;

The distance from B of the point both cars meet  = (140 - x) km

Given that both cars meet after one hour, we have;

The distance travelled by the second car coming from city B, after one hour = (140 - x) km = Speed of the second car × 1 hour

88.42 km/h × 1 hour = 88.42 km = (140 - x) km

x = 140 - 88.42 ≈ 51.58 km

The distance from A of the point the first car meet the second car = x = 51.58 km

The speed of car A = (The distance from A of the point the first car meet the second car)/(Time it takes both cars to meet)

∴ The speed of the first car = 51.58 km/(1 hour)

The speed of the first car = 51.58 km/h ≈ 50 km/h (Rounding up to the nearest 10th).

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

12cm

the answer is d