Two cars, A and B start from pretoria to polokwane respectively simultaneously and travel towards each other at constant speeds along the route.After meeting at a point between pretoria and polokwane,the two cars proceed to their respective destinations of polokwane and pretoria.car A reaches polokwane 40 minutes after the two cars have met and car B reaches pretoria 90 minutes after they have met.How long did it take car A to cover the distance between pretoria and polokwane? (5 marks)
Let the distance of polokwane from pretoria be x
Let the cars meet at p < x
If car A has speed a and B has speed b, then
p/a = (x-p)/b
(x-p)/a = 2/3
p/b = 3/2
The solution is not unique. We get
p = (3/5) x
a = p
b = 2/3 p
It takes A 100 minutes
With a little checking, you can see that it does not matter what the actual distance and speeds are, as long as they meet 3/5 of the way from Pretoria to Polokwane.
It then takes A 2/3 hr to cover 2/5 the distance. Thus, it takes 5/3 hr = 100 minutes to cover the whole distance.
To solve this problem, let's break down the information provided:
- Car A and Car B start from Pretoria and Polokwane simultaneously.
- They travel towards each other at constant speeds.
- They meet at a point between Pretoria and Polokwane.
- Car A reaches Polokwane 40 minutes after they have met.
- Car B reaches Pretoria 90 minutes after they have met.
To answer the question, we need to determine how long it took Car A to cover the distance between Pretoria and Polokwane.
Let's assign some variables to help us solve the problem:
- Let the distance between Pretoria and the meeting point be represented as D1.
- Let the distance between the meeting point and Polokwane be represented as D2.
- Let the speed of Car A be represented as SA.
- Let the speed of Car B be represented as SB.
- Let the time taken for Car A to cover the distance D1 be represented as TA.
- Let the time taken for Car B to cover the distance D2 be represented as TB.
We know that Car A took 40 minutes to reach Polokwane after they met, and Car B took 90 minutes to reach Pretoria after they met.
The time taken by Car A to cover the distance D1 should be equal to the time taken by Car B to cover the distance D2, as they both traveled at constant speeds.
Therefore, we can say:
TA = TB
We also know that:
- The total time taken by Car A is TA + 40 minutes (as Car A took 40 minutes to reach Polokwane after they met).
- The total time taken by Car B is TB + 90 minutes (as Car B took 90 minutes to reach Pretoria after they met).
Since they both traveled at constant speeds, we can use the formula:
Speed = Distance / Time
For Car A:
- Speed = SA
- Distance = D1 + D2 (the total distance between Pretoria and Polokwane)
- Time = TA + 40
For Car B:
- Speed = SB
- Distance = D1 + D2 (the total distance between Pretoria and Polokwane)
- Time = TB + 90
Since the speeds of both cars are constant, we can write equations for the speeds:
SA = (D1 + D2) / (TA + 40)
SB = (D1 + D2) / (TB + 90)
Since Car A traveled the same distance as Car B, we can equate the two equations:
(D1 + D2) / (TA + 40) = (D1 + D2) / (TB + 90)
Now we can simplify the equation:
(TA + 40) = (TB + 90)
Rearranging the equation:
TA = TB + 50
Since we know that TA = TB, we can substitute into the equation:
TB = TB + 50
Simplifying,
0 = 50
The equation 0 = 50 is not possible, which means there is no solution consistent with the information given in the problem. It seems there may be an error or missing information in the question.