A park and a museum, 2500 m apart, are situated between Tina's house and Zoe's house. The museum is halfway between the two houses and the park is closer to Zoe's house. Tina and Zoe left their homes at the same time and arrived at the park at the same time. Tina drove at a speed of 68 km/h while Zoe drove at a speed 17 km/h slower than Tina. Leaving your answer in kilometres,

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

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

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

(b)
Time that Tina took to travel to the park
= 5 ÷ 17
= ⁵₁₇ h

Distance that Tina travelled
= ⁵₁₇ x 68
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Zoe's house and the museum
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km