Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
Secondary 1 | Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
could someone help me with this?
Date Posted: 3 years ago
Views: 182
See 1 Answer
You'll need to find the LCM of 60 and 80 first.
60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 5 × 3 = 2² × 5 × 3
(Or even more quickly, 60 = 4 × 15 = 2² × 3 × 5)
80 = 2 × 40 = 2 × 2 × 20 = 2 × 2 × 2 × 10 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5
(Or even more quickly, 80 = 16 × 5 = 2⁴ × 5)
LCM = 2⁴ × 5 × 3 = 16 × 5 × 3 = 80 × 3 = 240
This means that after 240s, they will both be at the starting point again. (This is the answer for i)
ii)
Number of laps the faster car does in 240s = 240s ÷ 60s per lap
= 4
Number of laps the slower car does in 240s = 240s ÷ 80s per lap
= 3
So, for every 240s, the faster car does 1 lap more than the slower car, ans is 1 lap ahead of it. (4 - 1 = 3)
In order to be 5 laps ahead,
5 ÷ 1 = 5
They need to travel for 5 times/sets of 240s.
Time needed = 5 × 240s
= 1200s
= (1200 ÷ 60) min
= 20 min
60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 5 × 3 = 2² × 5 × 3
(Or even more quickly, 60 = 4 × 15 = 2² × 3 × 5)
80 = 2 × 40 = 2 × 2 × 20 = 2 × 2 × 2 × 10 = 2 × 2 × 2 × 2 × 5 = 2⁴ × 5
(Or even more quickly, 80 = 16 × 5 = 2⁴ × 5)
LCM = 2⁴ × 5 × 3 = 16 × 5 × 3 = 80 × 3 = 240
This means that after 240s, they will both be at the starting point again. (This is the answer for i)
ii)
Number of laps the faster car does in 240s = 240s ÷ 60s per lap
= 4
Number of laps the slower car does in 240s = 240s ÷ 80s per lap
= 3
So, for every 240s, the faster car does 1 lap more than the slower car, ans is 1 lap ahead of it. (4 - 1 = 3)
In order to be 5 laps ahead,
5 ÷ 1 = 5
They need to travel for 5 times/sets of 240s.
Time needed = 5 × 240s
= 1200s
= (1200 ÷ 60) min
= 20 min
360 Tutoring Program