A pharmacy and a bank, 1000 m apart, are situated between Eva's house and Shiyun's house. The bank is halfway between the two houses and the pharmacy is closer to Shiyun's house. Eva and Shiyun left their homes at the same time and arrived at the pharmacy at the same time. Eva drove at a speed of 60 km/h while Shiyun drove at a speed 15 km/h slower than Eva. Leaving your answer in kilometres,

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

(a)
Let the distance between Eva's house and Shiyun's house be 1 d.
Shiyun travelled = ¹₂ d - 1000 m
Eva travelled = ¹₂ d + 1000 m

Distance that Eva travelled more than Shiyun
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Eva took to travel to the pharmacy
= 2 ÷ 15
= ²₁₅ h

Distance that Eva travelled
= ²₁₅ x 60
= 8 km

1000 m = 1 km
1000 m = 1 km

Distance between Shiyun's house and the bank
= 8 - 1
= 7 km

Answer(s): (a) 2 km; (b) 7 km