A pharmacy and a bank, 500 m apart, are situated between Wendy's house and Kathy's house. The bank is halfway between the two houses and the pharmacy is closer to Kathy's house. Wendy and Kathy left their homes at the same time and arrived at the pharmacy at the same time. Wendy drove at a speed of 75 km/h while Kathy drove at a speed 20 km/h slower than Wendy. Leaving your answer in kilometres,

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

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

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

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

Distance that Wendy travelled
= ¹₂₀ x 75
= 3.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Kathy's house and the bank
= 3.75 - 0.5
= 3.25 km

Answer(s): (a) 1 km; (b) 3.25 km