A salon and a cafe, 2500 m apart, are situated between Emma's house and Tina's house. The cafe is halfway between the two houses and the salon is closer to Tina's house. Emma and Tina left their homes at the same time and arrived at the salon at the same time. Emma drove at a speed of 68 km/h while Tina drove at a speed 16 km/h slower than Emma. Leaving your answer in kilometres,

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

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

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

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

Distance that Emma travelled
= ⁵₁₆ x 68
= 21.25 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Tina's house and the cafe
= 21.25 - 2.5
= 18.75 km

Answer(s): (a) 5 km; (b) 18.75 km