A pharmacy and a bank, 500 m apart, are situated between Natalie's house and Raeann's house. The bank is halfway between the two houses and the pharmacy is closer to Raeann's house. Natalie and Raeann left their homes at the same time and arrived at the pharmacy at the same time. Natalie drove at a speed of 63 km/h while Raeann drove at a speed 15 km/h slower than Natalie. Leaving your answer in kilometres,

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

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

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

(b)
Time that Natalie took to travel to the pharmacy
= 1 ÷ 15
= ¹₁₅ h

Distance that Natalie travelled
= ¹₁₅ x 63
= 4.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Raeann's house and the bank
= 4.2 - 0.5
= 3.7 km

Answer(s): (a) 1 km; (b) 3.7 km