A pharmacy and a bank, 500 m apart, are situated between Emma's house and Betty's house. The bank is halfway between the two houses and the pharmacy is closer to Betty's house. Emma and Betty left their homes at the same time and arrived at the pharmacy at the same time. Emma drove at a speed of 66 km/h while Betty drove at a speed 10 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

(b)
Time that Emma took to travel to the pharmacy
= 1 ÷ 10
= ¹₁₀ h

Distance that Emma travelled
= ¹₁₀ x 66
= 6.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Betty's house and the bank
= 6.6 - 0.5
= 6.1 km

Answer(s): (a) 1 km; (b) 6.1 km