A park and a museum, 1500 m apart, are situated between Shannon's house and Gabby's house. The museum is halfway between the two houses
and the park is closer to Gabby's house. Shannon and Gabby left their homes at the same time and arrived at the park at the same time. Shannon drove at a speed of 65 km/h while Gabby drove at a speed 20 km/h slower than Shannon. Leaving your answer in kilometres,
- how much farther did Shannon travel than Gabby?
- how far is Gabby's house from the museum?
(a)
Let the distance between Shannon's house and Gabby's house be 1 d.
Gabby travelled =
12 d - 1500 m
Shannon travelled =
12 d + 1500 m
Distance that Shannon travelled more than Gabby
=
12 d + 1500 - (
12 d - 1500)
=
12 d + 1500 -
12 d + 1500
= 3000 m
= 3 km
(b)
Time that Shannon took to travel to the park
= 3 ÷ 20
=
320 h
Distance that Shannon travelled
=
320 x 65
= 9.75 km
1000 m = 1 km
1500 m = 1.5 km
Distance between Gabby's house and the museum
= 9.75 - 1.5
= 8.25 km
Answer(s): (a) 3 km; (b) 8.25 km