A pharmacy and a bank, 1500 m apart, are situated between Mary's house and Winnie's house. The bank is halfway between the two houses and the pharmacy is closer to Winnie's house. Mary and Winnie left their homes at the same time and arrived at the pharmacy at the same time. Mary drove at a speed of 60 km/h while Winnie drove at a speed 16 km/h slower than Mary. Leaving your answer in kilometres,

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

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

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

(b)
Time that Mary took to travel to the pharmacy
= 3 ÷ 16
= ³₁₆ h

Distance that Mary travelled
= ³₁₆ x 60
= 11.25 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Winnie's house and the bank
= 11.25 - 1.5
= 9.75 km

Answer(s): (a) 3 km; (b) 9.75 km