A pharmacy and a bank, 2000 m apart, are situated between Roshel's house and Opal's house. The bank is halfway between the two houses and the pharmacy is closer to Opal's house. Roshel and Opal left their homes at the same time and arrived at the pharmacy at the same time. Roshel drove at a speed of 69 km/h while Opal drove at a speed 15 km/h slower than Roshel. Leaving your answer in kilometres,

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

(a)
Let the distance between Roshel's house and Opal's house be 1 d.
Opal travelled = ¹₂ d - 2000 m
Roshel travelled = ¹₂ d + 2000 m

Distance that Roshel travelled more than Opal
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Roshel took to travel to the pharmacy
= 4 ÷ 15
= ⁴₁₅ h

Distance that Roshel travelled
= ⁴₁₅ x 69
= 18.4 km

1000 m = 1 km
2000 m = 2 km

Distance between Opal's house and the bank
= 18.4 - 2
= 16.4 km

Answer(s): (a) 4 km; (b) 16.4 km