A pharmacy and a bank, 1500 m apart, are situated between Shiyun's house and Fanny's house. The bank is halfway between the two houses and the pharmacy is closer to Fanny's house. Shiyun and Fanny left their homes at the same time and arrived at the pharmacy at the same time. Shiyun drove at a speed of 71 km/h while Fanny drove at a speed 20 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

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

(b)
Time that Shiyun took to travel to the pharmacy
= 3 ÷ 20
= ³₂₀ h

Distance that Shiyun travelled
= ³₂₀ x 71
= 10.65 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Fanny's house and the bank
= 10.65 - 1.5
= 9.15 km

Answer(s): (a) 3 km; (b) 9.15 km