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

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

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

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

(b)
Time that Min took to travel to the pharmacy
= 1 ÷ 20
= ¹₂₀ h

Distance that Min travelled
= ¹₂₀ x 65
= 3.25 km

1000 m = 1 km
500 m = 0.5 km

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

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