A pharmacy and a bank, 500 m apart, are situated between Xandra's house and Erika's house. The bank is halfway between the two houses and the pharmacy is closer to Erika's house. Xandra and Erika left their homes at the same time and arrived at the pharmacy at the same time. Xandra drove at a speed of 63 km/h while Erika drove at a speed 18 km/h slower than Xandra. Leaving your answer in kilometres,

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

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

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

(b)
Time that Xandra took to travel to the pharmacy
= 1 ÷ 18
= ¹₁₈ h

Distance that Xandra travelled
= ¹₁₈ x 63
= 3.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Erika's house and the bank
= 3.5 - 0.5
= 3 km

Answer(s): (a) 1 km; (b) 3 km