A pharmacy and a bank, 500 m apart, are situated between Opal's house and Jaslyn's house. The bank is halfway between the two houses and the pharmacy is closer to Jaslyn's house. Opal and Jaslyn left their homes at the same time and arrived at the pharmacy at the same time. Opal drove at a speed of 67 km/h while Jaslyn drove at a speed 20 km/h slower than Opal. Leaving your answer in kilometres,

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

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

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

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

Distance that Opal travelled
= ¹₂₀ x 67
= 3.35 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jaslyn's house and the bank
= 3.35 - 0.5
= 2.85 km

Answer(s): (a) 1 km; (b) 2.85 km