A pharmacy and a bank, 1500 m apart, are situated between Zoe's house and Jen's house. The bank is halfway between the two houses and the pharmacy is closer to Jen's house. Zoe and Jen left their homes at the same time and arrived at the pharmacy at the same time. Zoe drove at a speed of 68 km/h while Jen drove at a speed 17 km/h slower than Zoe. Leaving your answer in kilometres,

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

(a)
Let the distance between Zoe's house and Jen's house be 1 d.
Jen travelled = ¹₂ d - 1500 m
Zoe travelled = ¹₂ d + 1500 m

Distance that Zoe travelled more than Jen
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Zoe took to travel to the pharmacy
= 3 ÷ 17
= ³₁₇ h

Distance that Zoe travelled
= ³₁₇ x 68
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Jen's house and the bank
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km