A pharmacy and a bank, 500 m apart, are situated between Irene's house and Roshel's house. The bank is halfway between the two houses and the pharmacy is closer to Roshel's house. Irene and Roshel left their homes at the same time and arrived at the pharmacy at the same time. Irene drove at a speed of 78 km/h while Roshel drove at a speed 12 km/h slower than Irene. Leaving your answer in kilometres,

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

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

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

(b)
Time that Irene took to travel to the pharmacy
= 1 ÷ 12
= ¹₁₂ h

Distance that Irene travelled
= ¹₁₂ x 78
= 6.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Roshel's house and the bank
= 6.5 - 0.5
= 6 km

Answer(s): (a) 1 km; (b) 6 km