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

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

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

Distance that Shiyun travelled more than Jane
= 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 ÷ 10
= ³₁₀ h

Distance that Shiyun travelled
= ³₁₀ x 64
= 19.2 km

1000 m = 1 km
1500 m = 1.5 km

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

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