A pharmacy and a bank, 500 m apart, are situated between Emma's house and Natalie's house. The bank is halfway between the two houses and the pharmacy is closer to Natalie's house. Emma and Natalie left their homes at the same time and arrived at the pharmacy at the same time. Emma drove at a speed of 80 km/h while Natalie drove at a speed 16 km/h slower than Emma. Leaving your answer in kilometres,

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

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

Distance that Emma travelled more than Natalie
= 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 ÷ 16
= ¹₁₆ h

Distance that Emma travelled
= ¹₁₆ x 80
= 5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Natalie's house and the bank
= 5 - 0.5
= 4.5 km

Answer(s): (a) 1 km; (b) 4.5 km