A salon and a cafe, 1500 m apart, are situated between Winnie's house and Vanessa's house. The cafe is halfway between the two houses and the salon is closer to Vanessa's house. Winnie and Vanessa left their homes at the same time and arrived at the salon at the same time. Winnie drove at a speed of 80 km/h while Vanessa drove at a speed 16 km/h slower than Winnie. Leaving your answer in kilometres,

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

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

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

(b)
Time that Winnie took to travel to the salon
= 3 ÷ 16
= ³₁₆ h

Distance that Winnie travelled
= ³₁₆ x 80
= 15 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Vanessa's house and the cafe
= 15 - 1.5
= 13.5 km

Answer(s): (a) 3 km; (b) 13.5 km