A pharmacy and a bank, 500 m apart, are situated between Jane's house and Usha's house. The bank is halfway between the two houses and the pharmacy is closer to Usha's house. Jane and Usha left their homes at the same time and arrived at the pharmacy at the same time. Jane drove at a speed of 63 km/h while Usha drove at a speed 18 km/h slower than Jane. Leaving your answer in kilometres,

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

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

Distance that Jane travelled more than Usha
= 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 ÷ 18
= ¹₁₈ h

Distance that Jane travelled
= ¹₁₈ x 63
= 3.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Usha's house and the bank
= 3.5 - 0.5
= 3 km

Answer(s): (a) 1 km; (b) 3 km