A pharmacy and a bank, 500 m apart, are situated between Lucy's house and Gwen's house. The bank is halfway between the two houses and the pharmacy is closer to Gwen's house. Lucy and Gwen left their homes at the same time and arrived at the pharmacy at the same time. Lucy drove at a speed of 65 km/h while Gwen drove at a speed 20 km/h slower than Lucy. Leaving your answer in kilometres,

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

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

Distance that Lucy travelled more than Gwen
= 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 ÷ 20
= ¹₂₀ h

Distance that Lucy travelled
= ¹₂₀ x 65
= 3.25 km

1000 m = 1 km
500 m = 0.5 km

Distance between Gwen's house and the bank
= 3.25 - 0.5
= 2.75 km

Answer(s): (a) 1 km; (b) 2.75 km