A pharmacy and a bank, 1500 m apart, are situated between Gwen's house and Betty's house. The bank is halfway between the two houses and the pharmacy is closer to Betty's house. Gwen and Betty left their homes at the same time and arrived at the pharmacy at the same time. Gwen drove at a speed of 71 km/h while Betty drove at a speed 20 km/h slower than Gwen. Leaving your answer in kilometres,

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

(a)
Let the distance between Gwen's house and Betty's house be 1 d.
Betty travelled = ¹₂ d - 1500 m
Gwen travelled = ¹₂ d + 1500 m

Distance that Gwen travelled more than Betty
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Gwen took to travel to the pharmacy
= 3 ÷ 20
= ³₂₀ h

Distance that Gwen travelled
= ³₂₀ x 71
= 10.65 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Betty's house and the bank
= 10.65 - 1.5
= 9.15 km

Answer(s): (a) 3 km; (b) 9.15 km