A pharmacy and a bank, 1000 m apart, are situated between Nora's house and Vanessa's house. The bank is halfway between the two houses and the pharmacy is closer to Vanessa's house. Nora and Vanessa left their homes at the same time and arrived at the pharmacy at the same time. Nora drove at a speed of 72 km/h while Vanessa drove at a speed 15 km/h slower than Nora. Leaving your answer in kilometres,

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

(a)
Let the distance between Nora's house and Vanessa's house be 1 d.
Vanessa travelled = ¹₂ d - 1000 m
Nora travelled = ¹₂ d + 1000 m

Distance that Nora travelled more than Vanessa
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Nora took to travel to the pharmacy
= 2 ÷ 15
= ²₁₅ h

Distance that Nora travelled
= ²₁₅ x 72
= 9.6 km

1000 m = 1 km
1000 m = 1 km

Distance between Vanessa's house and the bank
= 9.6 - 1
= 8.6 km

Answer(s): (a) 2 km; (b) 8.6 km