A pharmacy and a bank, 1000 m apart, are situated between Tina's house and Cathy's house. The bank is halfway between the two houses and the pharmacy is closer to Cathy's house. Tina and Cathy left their homes at the same time and arrived at the pharmacy at the same time. Tina drove at a speed of 69 km/h while Cathy drove at a speed 15 km/h slower than Tina. Leaving your answer in kilometres,

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

(a)
Let the distance between Tina's house and Cathy's house be 1 d.
Cathy travelled = ¹₂ d - 1000 m
Tina travelled = ¹₂ d + 1000 m

Distance that Tina travelled more than Cathy
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Tina took to travel to the pharmacy
= 2 ÷ 15
= ²₁₅ h

Distance that Tina travelled
= ²₁₅ x 69
= 9.2 km

1000 m = 1 km
1000 m = 1 km

Distance between Cathy's house and the bank
= 9.2 - 1
= 8.2 km

Answer(s): (a) 2 km; (b) 8.2 km