A pharmacy and a bank, 500 m apart, are situated between Gabby's house and Zoe's house. The bank is halfway between the two houses and the pharmacy is closer to Zoe's house. Gabby and Zoe left their homes at the same time and arrived at the pharmacy at the same time. Gabby drove at a speed of 69 km/h while Zoe drove at a speed 12 km/h slower than Gabby. Leaving your answer in kilometres,

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

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

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

(b)
Time that Gabby took to travel to the pharmacy
= 1 ÷ 12
= ¹₁₂ h

Distance that Gabby travelled
= ¹₁₂ x 69
= 5.75 km

1000 m = 1 km
500 m = 0.5 km

Distance between Zoe's house and the bank
= 5.75 - 0.5
= 5.25 km

Answer(s): (a) 1 km; (b) 5.25 km