a ferrari and a porsche begin a race with a moving start and each car moves with constant speed. the ferrari laps overtakes the porsche after the porsche has completed 9 laps. if the speed of the ferrari had been 10 km/hr less the porsche would have traveled 18 laps before being overtaken. if needed a lap=2 km. what were the speeds of the two cars?

where exactly did you get the 38 and 36 from in the 2nd portion of the question?

To solve this problem, we need to set up equations based on the information given and then solve for the speeds of the two cars.

Let's assume the speed of the Ferrari is "F" km/hr and the speed of the Porsche is "P" km/hr.

Given information:
1. The Ferrari overtakes the Porsche after the Porsche has completed 9 laps.
2. If the speed of the Ferrari had been 10 km/hr less, the Porsche would have completed 18 laps before being overtaken.
3. 1 lap is equal to 2 km.

Let's now break down the information into equations:

Equation 1: The distance covered by the Ferrari when overtaking the Porsche is the same as the distance covered by the Porsche in 9 laps.
Distance covered by the Ferrari = Distance covered by the Porsche in 9 laps
Solving for distance:
(F * 9) = (P * 9) * 2 (since 1 lap = 2 km)

Equation 2: If the speed of the Ferrari were 10 km/hr less, the Porsche would have covered 18 laps before being overtaken.
Distance covered by the Ferrari = Distance covered by the Porsche in 18 laps
Solving for distance:
(F - 10) * 9 = (P * 18) * 2

We now have two equations:

(F * 9) = (P * 9) * 2
(F - 10) * 9 = (P * 18) * 2

We can now solve these equations to find the values of F and P.

By simplifying Equation 1, we get:
F = 2P

Substituting this value of F in Equation 2, we get:
(2P - 10) * 9 = (P * 18) * 2

Simplifying Equation 2, we get:
18P - 90 = 36P

Bringing like terms to one side, we get:
18P - 36P = 90

Simplifying further, we get:
-18P = 90

Dividing both sides of the equation by -18, we get:
P = -5

Since the speed of the car cannot be negative, this result is not valid.

Hence, there is no valid solution for the speeds of the two cars that satisfies the given conditions.

18 laps * 2 km =36 km

19 laps ....

Let

P = speed of Porsche
F = speed of Ferrari

The Ferrari makes 10 laps while the Porsche completed 9.
Thus,
20/F = 18/P
F = (20/18)P
F = (10/9)P ....(1)

If the Ferrari had been 10 km/h less, then it would have done 19 laps in the time the Porsche had done 18. Therefore
38/(F-10) = 36/P
36(F-10) = 38P
36F = 38P + 360 (2)

Substitute (1) in (2) and solve for F and P.