The distance between towns M and N is 280 km. A car and a lorry travel from M to N. 

The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N. 
(a) If the speed of the lorry is x km/h, find x 
(b) The lorry left town M at 8: 15 a.m. The car left town M later and overtook the lorry at 12.15 p.m. Calculate the time the car left town M.

speed of lorry ---- x km/h

speed of car ----- x+20 km/h

time for the car = 280/(x+20)
time for lorry = 280/x

280/x - 280/(x+20) = 70/60
divide by 70
4/x - 4/(x+20) = 1/60
times 60x(x+20), the LCD
240(x+20) - 240x = x(x+20)
240x + 4800 - 240x = x^2 + 20x
x^2 + 20x - 4800 = 0
(x - 60)(x + 80) = 0
x = 60 or x is a negative

the speed of the lorry is 60 km/h

b) at the time of overtaking, the lorry had gone for
4 hrs, thus it had gone 240 km
for the car to go those same 240 km would have taken 240/80 hrs or 3 hrs.
So just "backup" 3 hrs from 12:15

9:15 am

To solve this problem, let's first define some variables:

Let's assume the speed of the car is "c" km/h.

Then, the speed of the lorry is "c - 20" km/h (since it's 20 km/h less than the car).

The time taken by the car to travel from M to N is "t" hours.

The time taken by the lorry to travel from M to N is "t + 1 + 10/60" hours (since it takes 1 hour and 10 minutes more than the car).

The distance traveled by both the car and the lorry is the same, which is 280 km.

Now, let's solve the problem:

(a) To find the speed of the lorry, we can set up the equation:

Distance = Speed * Time

For the car: 280 = c * t

For the lorry: 280 = (c - 20) * (t + 1 + 10/60)

Now, we can solve these equations simultaneously:

280 = c * t

and

280 = (c - 20) * (t + 1 + 10/60)

Simplifying the second equation:

280 = (c - 20) * (t + 1.1667)

280 = c * t + 1.1667c - 20t - 23.334

Rearranging the terms:

c * t - 20t - 1.1667c = 280 - 23.334

Combining like terms:

t(c - 20) - 1.1667c = 256.666

Simplifying:

tc - 20t - 1.1667c = 256.666

Now, we have two variables (c and t) and one equation. We need another equation to solve for c.
Let's use the fact that the car overtakes the lorry at 12.15 p.m. to find another equation.

(b) The lorry left town M at 8:15 a.m., and the car overtakes the lorry at 12.15 p.m, which is 4 hours later. Therefore, the car takes t hours to overtake the lorry.

To find the time the car left town M, we can subtract t from 12.15 p.m:

12.15 p.m. - t

Now, we'll set this time equal to 8:15 a.m.:

12.15 - t = 8.15

Simplifying:

4 - t = 0.15

Adding t to both sides:

4 = 0.15 + t

Simplifying further:

t = 4 - 0.15

t = 3.85

Therefore, the car takes 3.85 hours or 3 hours and 51 minutes to overtake the lorry.

The time the car left town M can be calculated by subtracting this time from 12.15 p.m.:

12.15 - 3.85 = 8.30 a.m.

So, the car left town M at 8.30 a.m.

To find the value of x, we need to set up equations based on the given information.

Let's assume the average speed of the car is y km/h.
Given that the speed of the lorry is 20 km/h less than that of the car, we can express the speed of the lorry as (y - 20) km/h.

The time taken by the lorry to travel from M to N can be expressed as:
Time taken by lorry = Distance / Speed
Using the given information, the time taken by the lorry is 1 hour and 10 minutes longer than the car, which is 1 hour and 10/60 hours, or 7/6 hours.
So, we can set up the equation:

280 / (y - 20) = 280 / y + 7/6

To solve for x, we can cross-multiply and simplify:
280 * y = (280 * (y - 20)) + (7/6) * 280 * y
280y = 280y - 5600 + (7/6) * 280y
To solve for (7/6) * 280y
280y - (7/6) * 280y = 5600
Let's simplify and solve:
280y - 40y = 5600
240y = 5600
y = 5600 / 240
y = 23.33

Thus, the speed of the car (y) is approximately 23.33 km/h.

To find the time the car left town M, we need to consider the time it took the car to catch up to the lorry, which is 12:15 p.m. As the lorry left at 8:15 a.m., we can calculate the time interval:

12:15 p.m. - 8:15 a.m. = 4 hours

Therefore, the car left town M four hours after the lorry, which means the car left town M at 12:15 p.m. - 4 hours = 8:15 a.m.