A pharmacy and a bank, 2000 m apart, are situated between Tiffany's house and Rachel's house. The bank is halfway between the two houses and the pharmacy is closer to Rachel's house. Tiffany and Rachel left their homes at the same time and arrived at the pharmacy at the same time. Tiffany drove at a speed of 78 km/h while Rachel drove at a speed 15 km/h slower than Tiffany. Leaving your answer in kilometres,

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

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

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

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

Distance that Tiffany travelled
= ⁴₁₅ x 78
= 20.8 km

1000 m = 1 km
2000 m = 2 km

Distance between Rachel's house and the bank
= 20.8 - 2
= 18.8 km

Answer(s): (a) 4 km; (b) 18.8 km