A pharmacy and a bank, 500 m apart, are situated between Sarah's house and Elyse's house. The bank is halfway between the two houses and the pharmacy is closer to Elyse's house. Sarah and Elyse left their homes at the same time and arrived at the pharmacy at the same time. Sarah drove at a speed of 76 km/h while Elyse drove at a speed 20 km/h slower than Sarah. Leaving your answer in kilometres,

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

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

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

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

Distance that Sarah travelled
= ¹₂₀ x 76
= 3.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Elyse's house and the bank
= 3.8 - 0.5
= 3.3 km

Answer(s): (a) 1 km; (b) 3.3 km