, 2018

The distance from Botown to Aville is 120 km.
Jessica drove this distance at a speed of 90 km/h, and so it took Jessica $\dfrac{120}{90}=\dfrac43$ hours or $\dfrac43\times60=80$ minutes. The distance from Botown to Aville is 120 km. The car predicted that Jessica would drive this distance at a speed of 80 km/h, and so it predicted that it would take Jessica $\dfrac{120}{80}=\dfrac32$ hours or $\dfrac32\times60=90$ minutes. The ETA displayed by her car at 7:00 a.m. was 8:30 a.m.. Jessica drove from 7:00 a.m. to 7:16 a.m. (for 16 minutes) at a speed of 90 km/h, and so she travelled a distance of $\dfrac{16}{60}\times90=24$ km. At 7:16 a.m., Jessica had a distance of $\text{120 km -24 km =96 km}$ left to travel. The car predicted that Jessica would drive this distance at a speed of 80 km/h, and so it predicted that it would take Jessica $\dfrac{96}{80}=\dfrac65$ hours or $\dfrac65\times60=72$ minutes to complete the trip. The ETA displayed by her car at 7:16 a.m. was 72 minutes later or 8:28 a.m.. As in part (b), the car predicted that it would take Jessica 90 minutes or 1.5 hours to travel from Botown to Aville. Let the distance that Jessica travelled at 100 km/h be $d$ km, and so the distance that Jessica travelled at 50 km/h was $(120-d)$ km. The time that Jessica drove at 100 km/h was $\dfrac{d}{100}$ hours. The time that Jessica drove at 50 km/h was $\dfrac{120-d}{50}$ hours. Since the time predicted by her car is equal to the actual time that it took Jessica to travel from Botown to Aville, then $\dfrac{d}{100}+\dfrac{120-d}{50}=1.5$. Solving for $d$, we get $d+2(120-d)=1.5\times100$ or $-d+240=150$, and so $d=90$ km. Therefore, Jessica drove a distance of $90$ km at a speed of 100 km/h.