Question

1. deux autobus relient deux villes, a et b, distantes de 80 km. lautobus a fait le trajet ab alors que lautobus b fait le trajet inverse ba. a t = 0 s, lautobus a démarre et roule à une vitesse moyenne de 80 km/h. a t = 15 min, lautobus b démarre à son tour et roule à 120 km/h.

a) a quelle distance de la ville a les autobus vont - ils se rencontrer ?

Explanation:

Step1: Convert time unit

First, convert 15 minutes to hours. Since 1 hour = 60 minutes, $t_1=15\ min=\frac{15}{60}h = 0.25h$.

Step2: Calculate distance traveled by bus A in 15 minutes

Bus A has a speed $v_A = 80\ km/h$. The distance $d_1$ it travels in $t_1 = 0.25h$ is given by the formula $d=v\times t$. So $d_1=v_A\times t_1=80\times0.25 = 20\ km$.

Step3: Calculate relative - speed of the two - buses

After 15 minutes, bus B starts. The relative - speed of the two buses when they are both moving is $v = v_A + v_B$, where $v_A = 80\ km/h$ and $v_B = 120\ km/h$. So $v=80 + 120=200\ km/h$.

Step4: Calculate the remaining distance

The total distance between the two cities is 80 km. After bus A has traveled 20 km, the remaining distance $d_2$ is $d_2=80 - 20=60\ km$.

Step5: Calculate the time until they meet after bus B starts

Using the formula $t=\frac{d}{v}$, with $d = d_2 = 60\ km$ and $v = 200\ km/h$, we get $t_2=\frac{60}{200}=0.3h$.

Step6: Calculate the distance from city A when they meet

The total distance $d$ from city A when they meet is the distance bus A has traveled in the first 15 minutes plus the distance it travels in $t_2$. The distance bus A travels in $t_2$ is $d_A'=v_A\times t_2=80\times0.3 = 24\ km$. So $d=d_1 + d_A'=20+24 = 44\ km$.

Answer:

44 km