A park and a museum, 1500 m apart, are situated between Roshel's house and Barbara's house. The museum is halfway between the two houses
and the park is closer to Barbara's house. Roshel and Barbara left their homes at the same time and arrived at the park at the same time. Roshel drove at a speed of 60 km/h while Barbara drove at a speed 10 km/h slower than Roshel. Leaving your answer in kilometres,
- how much farther did Roshel travel than Barbara?
- how far is Barbara's house from the museum?
(a)
Let the distance between Roshel's house and Barbara's house be 1 d.
Barbara travelled =
12 d - 1500 m
Roshel travelled =
12 d + 1500 m
Distance that Roshel travelled more than Barbara
=
12 d + 1500 - (
12 d - 1500)
=
12 d + 1500 -
12 d + 1500
= 3000 m
= 3 km
(b)
Time that Roshel took to travel to the park
= 3 ÷ 10
=
310 h
Distance that Roshel travelled
=
310 x 60
= 18 km
1000 m = 1 km
1500 m = 1.5 km
Distance between Barbara's house and the museum
= 18 - 1.5
= 16.5 km
Answer(s): (a) 3 km; (b) 16.5 km