A salon and a cafe, 2000 m apart, are situated between Tammy's house and Hilda's house. The cafe is halfway between the two houses and the salon is closer to Hilda's house. Tammy and Hilda left their homes at the same time and arrived at the salon at the same time. Tammy drove at a speed of 69 km/h while Hilda drove at a speed 15 km/h slower than Tammy. Leaving your answer in kilometres,

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

(a)
Let the distance between Tammy's house and Hilda's house be 1 d.
Hilda travelled = ¹₂ d - 2000 m
Tammy travelled = ¹₂ d + 2000 m

Distance that Tammy travelled more than Hilda
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Tammy took to travel to the salon
= 4 ÷ 15
= ⁴₁₅ h

Distance that Tammy travelled
= ⁴₁₅ x 69
= 18.4 km

1000 m = 1 km
2000 m = 2 km

Distance between Hilda's house and the cafe
= 18.4 - 2
= 16.4 km

Answer(s): (a) 4 km; (b) 16.4 km