A pharmacy and a bank, 500 m apart, are situated between Pamela's house and Sarah's house. The bank is halfway between the two houses and the pharmacy is closer to Sarah's house. Pamela and Sarah left their homes at the same time and arrived at the pharmacy at the same time. Pamela drove at a speed of 62 km/h while Sarah drove at a speed 20 km/h slower than Pamela. Leaving your answer in kilometres,

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

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

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

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

Distance that Pamela travelled
= ¹₂₀ x 62
= 3.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Sarah's house and the bank
= 3.1 - 0.5
= 2.6 km

Answer(s): (a) 1 km; (b) 2.6 km