A salon and a cafe, 2500 m apart, are situated between Anna's house and Vanessa's house. The cafe is halfway between the two houses and the salon is closer to Vanessa's house. Anna and Vanessa left their homes at the same time and arrived at the salon at the same time. Anna drove at a speed of 72 km/h while Vanessa drove at a speed 16 km/h slower than Anna. Leaving your answer in kilometres,

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

(a)
Let the distance between Anna's house and Vanessa's house be 1 d.
Vanessa travelled = ¹₂ d - 2500 m
Anna travelled = ¹₂ d + 2500 m

Distance that Anna travelled more than Vanessa
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Anna took to travel to the salon
= 5 ÷ 16
= ⁵₁₆ h

Distance that Anna travelled
= ⁵₁₆ x 72
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Vanessa's house and the cafe
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km