A pharmacy and a bank, 1500 m apart, are situated between Xylia's house and Cindy's house. The bank is halfway between the two houses and the pharmacy is closer to Cindy's house. Xylia and Cindy left their homes at the same time and arrived at the pharmacy at the same time. Xylia drove at a speed of 64 km/h while Cindy drove at a speed 10 km/h slower than Xylia. Leaving your answer in kilometres,

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

(a)
Let the distance between Xylia's house and Cindy's house be 1 d.
Cindy travelled = ¹₂ d - 1500 m
Xylia travelled = ¹₂ d + 1500 m

Distance that Xylia travelled more than Cindy
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Xylia took to travel to the pharmacy
= 3 ÷ 10
= ³₁₀ h

Distance that Xylia travelled
= ³₁₀ x 64
= 19.2 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Cindy's house and the bank
= 19.2 - 1.5
= 17.7 km

Answer(s): (a) 3 km; (b) 17.7 km