A pharmacy and a bank, 500 m apart, are situated between Barbara's house and Eva's house. The bank is halfway between the two houses and the pharmacy is closer to Eva's house. Barbara and Eva left their homes at the same time and arrived at the pharmacy at the same time. Barbara drove at a speed of 64 km/h while Eva drove at a speed 20 km/h slower than Barbara. Leaving your answer in kilometres,

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

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

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

(b)
Time that Barbara took to travel to the pharmacy
= 1 ÷ 20
= ¹₂₀ h

Distance that Barbara travelled
= ¹₂₀ x 64
= 3.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Eva's house and the bank
= 3.2 - 0.5
= 2.7 km

Answer(s): (a) 1 km; (b) 2.7 km