A pharmacy and a bank, 1500 m apart, are situated between Xylia's house and Vanessa's house. The bank is halfway between the two houses and the pharmacy is closer to Vanessa's house. Xylia and Vanessa left their homes at the same time and arrived at the pharmacy at the same time. Xylia drove at a speed of 80 km/h while Vanessa drove at a speed 16 km/h slower than Xylia. Leaving your answer in kilometres,

1. how much farther did Xylia travel than Vanessa?
2. how far is Vanessa's house from the bank?

(a)
Let the distance between Xylia's house and Vanessa's house be 1 d.
Vanessa travelled = ¹₂ d - 1500 m
Xylia travelled = ¹₂ d + 1500 m

Distance that Xylia travelled more than Vanessa
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Xylia took to travel to the pharmacy
= 3 ÷ 16
= ³₁₆ h

Distance that Xylia travelled
= ³₁₆ x 80
= 15 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Vanessa's house and the bank
= 15 - 1.5
= 13.5 km

Answer(s): (a) 3 km; (b) 13.5 km