constant speed

During the first 30 minutes of a journey Dora drove at a constant speed. During the following 30 minutes she drove at a constant speed but 20 km/h faster. If her total distance travelled was 100 km , how fast did she travel in the first 30 minutes.

the only think i know here is that the speed is the distance she covered divided to the time she got to do this distance.

i know that the total distance she covered is 100 km in an hour so the speed should be 100km/h . but because the second half she was 20 km/h faster than the first half i could say that the first half the speed should be 80 km/h.

the right answer is 90 km/h. how do i should think to get the correct answer.

No that is not right. You can´t do it that way because the distance is different for the two speeds/velocitys. You need to do an equation.

You say you know speed is $\frac{d i s \tan c e}{t i m e}$

It is more useful that $d i s \tan c e = s p e e d \cdot t i m e$ .

For the first 30 minutes, we don´t know her speed. We call it "x".

For the next 30 minutes, her speed was 20 km/h faster, therefor we call it "x+20"

Can you set up an equation with this with the fact that distance= speed * time?

Solution in spoiler

Visa spoiler

Distance for the first 30 minutes=0,5 hours.

Time is 30 minutes. Speed is x. So distance becomes $x \cdot 0, 5 = 0, 5 x$

Distance for the next 30 minutes

¨Time is 30 minutes, Speed is x+20. So distance becomes $0, 5 \cdot (x + 20) = 0, 5 x + 10$

Total distance is $0, 5 x + 0, 5 x + 10$

And we know the total distance was 100 km

$0, 5 x + 0, 5 x + 10 = 100 x = 90$

Thank you for your super help.

Svara