A pharmacy and a bank, 500 m apart, are situated between Lucy's house and Xandra's house. The bank is halfway between the two houses and the pharmacy is closer to Xandra's house. Lucy and Xandra left their homes at the same time and arrived at the pharmacy at the same time. Lucy drove at a speed of 72 km/h while Xandra drove at a speed 16 km/h slower than Lucy. Leaving your answer in kilometres,

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

(a)
Let the distance between Lucy's house and Xandra's house be 1 d.
Xandra travelled = ¹₂ d - 500 m
Lucy travelled = ¹₂ d + 500 m

Distance that Lucy travelled more than Xandra
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Lucy took to travel to the pharmacy
= 1 ÷ 16
= ¹₁₆ h

Distance that Lucy travelled
= ¹₁₆ x 72
= 4.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Xandra's house and the bank
= 4.5 - 0.5
= 4 km

Answer(s): (a) 1 km; (b) 4 km