A pharmacy and a bank, 1500 m apart, are situated between Xandra's house and Shannon's house. The bank is halfway between the two houses and the pharmacy is closer to Shannon's house. Xandra and Shannon left their homes at the same time and arrived at the pharmacy at the same time. Xandra drove at a speed of 77 km/h while Shannon drove at a speed 11 km/h slower than Xandra. Leaving your answer in kilometres,

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

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

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

(b)
Time that Xandra took to travel to the pharmacy
= 3 ÷ 11
= ³₁₁ h

Distance that Xandra travelled
= ³₁₁ x 77
= 21 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Shannon's house and the bank
= 21 - 1.5
= 19.5 km

Answer(s): (a) 3 km; (b) 19.5 km