X=v.t problem?

Question

the distance between A and B is 100 km .
B is east of A.
2 vehicles start travelling at the same time,one from A and the other from B.
Both go east.
they meet after 10 hours.
the vehicle that started from B goes 4 km in (t+2 minutes) time when the vehicle started at A goes 4 km in t time.
what are the speeds of the 2 vehicles?

I know the answer is 30,40 km/hour .
I need the way

Answer 1

The speed of the vehicle starting from B in Km per minute is 4/(t + 2)

The speed of the one starting from A is 4/t

When they meet after 10 hours (600 minutes), the distance done by the car starting from A is
600 * 4/t

The distance done by the car starting from B is 100 Km less 600 * 4/t - 100 or 600 * 4/(t + 2)

600 * 4/t -100 = 600 * 4/(t + 2)

2400/t - 100 = 2400/(t + 2) // Multiply by t(t + 2)

2400(t + 2) - 100t(t + 2) = 2400t

2400t + 4800 - 100t(t + 2) = 2400t // - 2400t

4800 - 100t(t + 2) = 0

-4800 + 100t(t + 2) = 0

-4800 + 100t^2 + 200t = 0

100t^2 + 200t - 4800 = 0 / divide by 100

t^2 + 2t - 48 = 0

Completing the square to solve a quadratic equation:

t^2 + 2t + 1 -1 - 48 = 0

(t + 1)^2 - 49 = 0

(t + 1 + 7)(t - 1 - 7) = 0

(t + 8)(t - 6) = 0

t=6

Now, the vehicle starting from A travels at
4/t = 4/6 Km per minute = 4*60/6 Km/h = 40Km/h

The vehicle starting from B travels at 4/(t + 2) =
= 4/8 Km per minute = 4*60/8 Km/h = 30 Km/h