A park and a museum, 500 m apart, are situated between Tammy's house and Joelle's house. The museum is halfway between the two houses and the park is closer to Joelle's house. Tammy and Joelle left their homes at the same time and arrived at the park at the same time. Tammy drove at a speed of 77 km/h while Joelle drove at a speed 14 km/h slower than Tammy. Leaving your answer in kilometres,

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

(a)
Let the distance between Tammy's house and Joelle's house be 1 d.
Joelle travelled = ¹₂ d - 500 m
Tammy travelled = ¹₂ d + 500 m

Distance that Tammy travelled more than Joelle
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Tammy took to travel to the park
= 1 ÷ 14
= ¹₁₄ h

Distance that Tammy travelled
= ¹₁₄ x 77
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Joelle's house and the museum
= 5.5 - 0.5
= 5 km

Answer(s): (a) 1 km; (b) 5 km