A pharmacy and a bank, 2500 m apart, are situated between Rachel's house and Victoria's house. The bank is halfway between the two houses and the pharmacy is closer to Victoria's house. Rachel and Victoria left their homes at the same time and arrived at the pharmacy at the same time. Rachel drove at a speed of 64 km/h while Victoria drove at a speed 16 km/h slower than Rachel. Leaving your answer in kilometres,

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

(a)
Let the distance between Rachel's house and Victoria's house be 1 d.
Victoria travelled = ¹₂ d - 2500 m
Rachel travelled = ¹₂ d + 2500 m

Distance that Rachel travelled more than Victoria
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Rachel took to travel to the pharmacy
= 5 ÷ 16
= ⁵₁₆ h

Distance that Rachel travelled
= ⁵₁₆ x 64
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Victoria's house and the bank
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km