A pharmacy and a bank, 2500 m apart, are situated between Tiffany's house and Kylie's house. The bank is halfway between the two houses and the pharmacy is closer to Kylie's house. Tiffany and Kylie left their homes at the same time and arrived at the pharmacy at the same time. Tiffany drove at a speed of 72 km/h while Kylie drove at a speed 16 km/h slower than Tiffany. Leaving your answer in kilometres,

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

(a)
Let the distance between Tiffany's house and Kylie's house be 1 d.
Kylie travelled = ¹₂ d - 2500 m
Tiffany travelled = ¹₂ d + 2500 m

Distance that Tiffany travelled more than Kylie
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Tiffany took to travel to the pharmacy
= 5 ÷ 16
= ⁵₁₆ h

Distance that Tiffany travelled
= ⁵₁₆ x 72
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Kylie's house and the bank
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km