A pharmacy and a bank, 1500 m apart, are situated between Xylia's house and Tiffany's house. The bank is halfway between the two houses and the pharmacy is closer to Tiffany's house. Xylia and Tiffany left their homes at the same time and arrived at the pharmacy at the same time. Xylia drove at a speed of 66 km/h while Tiffany drove at a speed 10 km/h slower than Xylia. Leaving your answer in kilometres,

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

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

Distance that Xylia travelled more than Tiffany
= 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 ÷ 10
= ³₁₀ h

Distance that Xylia travelled
= ³₁₀ x 66
= 19.8 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Tiffany's house and the bank
= 19.8 - 1.5
= 18.3 km

Answer(s): (a) 3 km; (b) 18.3 km