A pharmacy and a bank, 500 m apart, are situated between Jane's house and Jen's house. The bank is halfway between the two houses and the pharmacy is closer to Jen's house. Jane and Jen left their homes at the same time and arrived at the pharmacy at the same time. Jane drove at a speed of 72 km/h while Jen drove at a speed 15 km/h slower than Jane. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jane took to travel to the pharmacy
= 1 ÷ 15
= ¹₁₅ h

Distance that Jane travelled
= ¹₁₅ x 72
= 4.8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jen's house and the bank
= 4.8 - 0.5
= 4.3 km

Answer(s): (a) 1 km; (b) 4.3 km