what value of m will make 4x-7y=5 and 9x+my=3 parallel?

a car leaves town A at 10:00 a.m. and travels at a constant speed of 40 kph towards a town B. After 30 minutes, a bus leaves town A and travels towards town B at a constant speed of 56 kph. at what time will the bus catch up with the car and how far will they be from town A?

two towns A and B are 35 km apart. Carlo starts cycling from A towards B at 1:00 p.m. at 20 kph intil he is 16 kilometers away from A, when he changes his speed so that he arrives at B at 3:00 p.m. his friend Arnold leaves town B at 1:30 pm and cycles towards town A at a constant speed of 25 kph.find: a) carlo's speed in the last part of the journey. b) the time when Arnold reachestown A. c) the time when the two men meet.

Parallel lines have the same gradient.

The gradient of the first line is: 4/7

The gradient of the second line is: -9/m

Thus: 4/7 = -9/m

Solve for: m = ...

distance = speed multiplied by time.

Measure all distance in kilometres and all time in hours.

The car travels: c(t) = 40 t
The bus travels: b(t) = 56 (t - 0.5)

Solve for t when c(t)=b(t)

find: a) carlo's speed in the last part of the journey.

Carlos travels 16km at 20kph for: 20/16 hours.

Thus Carlos travels the remaining (35-16) km for (2-20/16)hours at:
(35-16)/(2-20/16)kph.

b) the time when Arnold reaches town A.

Arnold travels 35km at 25kph for: (35/25)hours.
Thus arriving at his destination at:
1:30+(35/25)

c) the time when the two men meet.
At 1:00+20/16 (when Carlos changes speed 16 km from A), Arnold has traveled:
((1+20/15)-1.5)25 kilometres.

Thus they have already passed.

At the time t they meet:
Arnold has traveled (t-1.5)25 kilometres
Carlos has yet to travel: (3-t)(35-16)/(2-20/16)

Solve: (t-1.5)25 = (3-t)(35-16)/(2-20/16)

To find the value of m that will make the given equations parallel, we need to compare their coefficients.

For the given equations:
4x - 7y = 5 --- Equation 1
9x + my = 3 --- Equation 2

To determine if two lines are parallel, their slope (the coefficient of x) must be equal.

So, let's equate the coefficients of x in the two equations:
4 = 9 (Since both coefficients of x must be equal for parallel lines)

This equation is not true, which means there is no value of m that will make the two equations parallel.

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To find the time and distance when the bus catches up to the car, we need to consider their respective speeds and the time difference.

Given:
Car's speed = 40 kph
Bus's speed = 56 kph
Time difference = 30 minutes = 0.5 hours

Let's assume the time it takes for the bus to catch up to the car is t hours.

Now, we can set up an equation to represent the distance traveled by both vehicles:
Distance covered by the car = Distance covered by the bus

The distance covered by the car can be found using the formula: Distance = Speed × Time
Distance of the car = 40t

The distance covered by the bus is the distance covered by the car, minus the distance they are apart initially: Distance of the bus = 40t - 35

Since both distances should be equal:
40t = 40t - 35

Now, let's solve for t:
35 = 0
This equation is not possible to solve.

Therefore, the bus will never catch up to the car.

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To find the answers for the given scenarios involving Carlo and Arnold, we can use the formula: Distance = Speed × Time.

Given:
Distance between town A and town B = 35 km

a) To find Carlo's speed in the last part of the journey, we need to know the distance he covers in that part. We can calculate it by subtracting the distance he covers initially (16 km) from the total distance between the towns (35 km):
Distance covered in the last part of the journey = 35 km - 16 km = 19 km

Now, let's calculate Carlo's speed using the formula: Speed = Distance / Time.
Speed = 19 km / (2 hours - 1 hour)
Speed = 19 km / 1 hour
Speed = 19 km/h

Therefore, Carlo's speed in the last part of the journey is 19 km/h.

b) Arnold leaves town B at 1:30 pm and cycles towards town A at a constant speed of 25 kph. To find when Arnold reaches town A, we need to calculate the time it takes him to cover the distance between the towns (35 km).

Time = Distance / Speed
Time = 35 km / 25 kph
Time = 7/5 hours

Converting 7/5 hours to minutes:
7/5 * 60 = 84 minutes

Therefore, Arnold will reach town A 1 hour and 24 minutes after he starts, which is at 2:54 pm.

c) To find the time when the two men meet, we need to find out how long Carlo has been cycling before Arnold starts.

Arnold starts 30 minutes (0.5 hours) after Carlo:
Time difference = 0.5 hours

Now, let's calculate the meeting time using the formula: Distance = Speed × Time.
Carlo's distance = 16 km
Arnold's distance = Distance between the towns - Carlo's distance = 35 km - 16 km = 19 km

Let's calculate the meeting time:
Time = Distance / Speed
Time = 19 km / (20 kph + 25 kph)
Time = 19 km / 45 kph
Time = 19/45 hours

Converting 19/45 hours to minutes:
19/45 * 60 = 25.33 minutes

Therefore, the two men will meet approximately 25.33 minutes after Arnold starts, which corresponds to about 1:55 pm.