A pharmacy and a bank, 1500 m apart, are situated between Fiona's house and Shiyun's house. The bank is halfway between the two houses and the pharmacy is closer to Shiyun's house. Fiona and Shiyun left their homes at the same time and arrived at the pharmacy at the same time. Fiona drove at a speed of 70 km/h while Shiyun drove at a speed 14 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

(b)
Time that Fiona took to travel to the pharmacy
= 3 ÷ 14
= ³₁₄ h

Distance that Fiona travelled
= ³₁₄ x 70
= 15 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Shiyun's house and the bank
= 15 - 1.5
= 13.5 km

Answer(s): (a) 3 km; (b) 13.5 km