A pharmacy and a bank, 500 m apart, are situated between Anna's house and Yen's house. The bank is halfway between the two houses and the pharmacy is closer to Yen's house. Anna and Yen left their homes at the same time and arrived at the pharmacy at the same time. Anna drove at a speed of 77 km/h while Yen drove at a speed 20 km/h slower than Anna. Leaving your answer in kilometres,

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

(a)
Let the distance between Anna's house and Yen's house be 1 d.
Yen travelled = ¹₂ d - 500 m
Anna travelled = ¹₂ d + 500 m

Distance that Anna travelled more than Yen
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Anna took to travel to the pharmacy
= 1 ÷ 20
= ¹₂₀ h

Distance that Anna travelled
= ¹₂₀ x 77
= 3.85 km

1000 m = 1 km
500 m = 0.5 km

Distance between Yen's house and the bank
= 3.85 - 0.5
= 3.35 km

Answer(s): (a) 1 km; (b) 3.35 km