A pharmacy and a bank, 500 m apart, are situated between Gwen's house and Erika's house. The bank is halfway between the two houses and the pharmacy is closer to Erika's house. Gwen and Erika left their homes at the same time and arrived at the pharmacy at the same time. Gwen drove at a speed of 69 km/h while Erika drove at a speed 12 km/h slower than Gwen. Leaving your answer in kilometres,

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

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

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

(b)
Time that Gwen took to travel to the pharmacy
= 1 ÷ 12
= ¹₁₂ h

Distance that Gwen travelled
= ¹₁₂ x 69
= 5.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Erika's house and the bank
= 5.75 - 0.5
= 5.25 km

Answer(s): (a) 1 km; (b) 5.25 km