A car travels 20 km/h faster than a truck. The car covers 360 km in 3 hours less time than the truck.Find the speed of the truck.

(kindly write the solution, thanks alot)

vc = vt + 20

tc = tt - 3

360 = vc tc = (vt+20)(tt-3)
360 = vt tt so tt = 360/vt

360 = (vt+20)(360/vt - 3)

360 vt = (vt+20)(-3 vt +360)
360 vt = -3 vt^2 -60 vt + 360 vt + 7200

3 vt^2 + 60 vt -7200 = 0
vt^2 + 20 vt - 2400 = 0
(vt+60)(vt-40) = 0
vt = 40

sir what do you mean by vt and tt, vc and tc... tnx....

yeah

To find the speed of the truck, we can break down the given information into equations.

Let's say the speed of the truck is x km/h.

According to the problem, the car travels 20 km/h faster than the truck, so the speed of the car is x + 20 km/h.

The time taken by the car to cover a distance of 360 km is 3 hours less than the time taken by the truck.

We can use the formula: Speed = Distance / Time

For the truck: x = 360 / (Time taken by the truck)

For the car: x + 20 = 360 / (Time taken by the truck - 3)

Solving these two equations, we can find the value of x, which is the speed of the truck.

Let's solve the equations step by step:

1. x = 360 / (Time taken by the truck)

2. x + 20 = 360 / (Time taken by the truck - 3)

We can start by simplifying equation 1:

x * (Time taken by the truck) = 360

Now, let's solve equation 2:

(x + 20) * (Time taken by the truck - 3) = 360

Expanding equation 2:

x * (Time taken by the truck) - 3x + 20 * (Time taken by the truck) - 60 = 360

Combining like terms in equation 2:

x * (Time taken by the truck) + 20 * (Time taken by the truck) - 3x - 60 = 360

Simplifying equation 2 further:

21 * (Time taken by the truck) - 3x - 60 = 360

Now, let's substitute the value of x from equation 1 into equation 2:

21 * (Time taken by the truck) - 3 * (360 / (Time taken by the truck)) - 60 = 360

Multiplying through by (Time taken by the truck):

21 * (Time taken by the truck)^2 - 3 * 360 - 60 * (Time taken by the truck) = 360 * (Time taken by the truck)

Rearranging the terms:

21 * (Time taken by the truck)^2 - 60 * (Time taken by the truck) - 3 * 360 - 360 * (Time taken by the truck) = 0

Simplifying further:

21 * (Time taken by the truck)^2 - 420 * (Time taken by the truck) - 1080 = 0

Now, we have a quadratic equation in terms of (Time taken by the truck), let's solve it using the quadratic formula:

(Time taken by the truck) = (-b ± √(b^2 - 4ac)) / 2a

Where a = 21, b = -420, and c = -1080.

Plugging in the values:

(Time taken by the truck) = (-(-420) ± √((-420)^2 - 4 * 21 * (-1080))) / (2 * 21)

(Time taken by the truck) = (420 ± √(176400 + 90720)) / 42

(Time taken by the truck) = (420 ± √(267120)) / 42

(Time taken by the truck) = (420 ± 516.89) / 42

Now, we have two possible values for (Time taken by the truck):

1. (Time taken by the truck) = (420 + 516.89) / 42 = 936.89 / 42 = 22.3 hours

2. (Time taken by the truck) = (420 - 516.89) / 42 = -96.89 / 42 ≈ -2.31 hours

Since time cannot be negative in this context, we discard the second solution.

Therefore, the speed of the truck is x = 360 / (Time taken by the truck) = 360 / 22.3 ≈ 16.1 km/h

Hence, the speed of the truck is approximately 16.1 km/h.