A park and a museum, 1500 m apart, are situated between Xylia's house and Tina's house. The museum is halfway between the two houses
and the park is closer to Tina's house. Xylia and Tina left their homes at the same time and arrived at the park at the same time. Xylia drove at a speed of 76 km/h while Tina drove at a speed 20 km/h slower than Xylia. Leaving your answer in kilometres,
- how much farther did Xylia travel than Tina?
- how far is Tina's house from the museum?
(a)
Let the distance between Xylia's house and Tina's house be 1 d.
Tina travelled =
12 d - 1500 m
Xylia travelled =
12 d + 1500 m
Distance that Xylia travelled more than Tina
=
12 d + 1500 - (
12 d - 1500)
=
12 d + 1500 -
12 d + 1500
= 3000 m
= 3 km
(b)
Time that Xylia took to travel to the park
= 3 ÷ 20
=
320 h
Distance that Xylia travelled
=
320 x 76
= 11.4 km
1000 m = 1 km
1500 m = 1.5 km
Distance between Tina's house and the museum
= 11.4 - 1.5
= 9.9 km
Answer(s): (a) 3 km; (b) 9.9 km