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primary 6 | Maths
| Speed
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Hi. Please help to solve and explain. Thank you!
Date Posted: 4 years ago
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a)
Tom takes 7 min to run a round. So in 2 min , he ran 2/7 of the round.
Now he met Kelvin there. Since 1 - 2/7 = 5/7, Tom has 5/7 of the round left to complete. This also means Kelvin completed 5/7 of the round in 2 min but Kelvin did so in the reverse direction.
After 4 min from the start, Tom completed 4/7 of the round. 1 - 4/7 = 3/7 so he has 3/7 left to complete. He met Bob there so this means Bob completed 3/7 of the round in 4 min, but in the reverse direction.
So Bob's ran 3/7 of round in 4 min.
Tom ran 4/7 of round in 4 min.
Kelvin ran 5/7 of round in 2 min, so in 4 min, he ran twice of that.
He ran 5/7 x 2 = 10/7 or 1 3/7 of a round in 4 min.
Since time is taken is the same for all 3 in this comparison, we just compare the numerators of the fractions.
We can say that a round's distance is 7 units. In 4 mins Tom ran 4 units, Bob ran 3 units and Kelvin ran 10 units.
To find their speed we would divide by 4 or multiply by ¼, to get the distance per minute. But since the ratio would still be the same as we are dividing/multiplying the same way for all 3 fractions, we can just directly compare the units for the required ratio.
Ratio of Tom's speed to Kelvin's to Bob's = 4 : 10 : 3
Tom takes 7 min to run a round. So in 2 min , he ran 2/7 of the round.
Now he met Kelvin there. Since 1 - 2/7 = 5/7, Tom has 5/7 of the round left to complete. This also means Kelvin completed 5/7 of the round in 2 min but Kelvin did so in the reverse direction.
After 4 min from the start, Tom completed 4/7 of the round. 1 - 4/7 = 3/7 so he has 3/7 left to complete. He met Bob there so this means Bob completed 3/7 of the round in 4 min, but in the reverse direction.
So Bob's ran 3/7 of round in 4 min.
Tom ran 4/7 of round in 4 min.
Kelvin ran 5/7 of round in 2 min, so in 4 min, he ran twice of that.
He ran 5/7 x 2 = 10/7 or 1 3/7 of a round in 4 min.
Since time is taken is the same for all 3 in this comparison, we just compare the numerators of the fractions.
We can say that a round's distance is 7 units. In 4 mins Tom ran 4 units, Bob ran 3 units and Kelvin ran 10 units.
To find their speed we would divide by 4 or multiply by ¼, to get the distance per minute. But since the ratio would still be the same as we are dividing/multiplying the same way for all 3 fractions, we can just directly compare the units for the required ratio.
Ratio of Tom's speed to Kelvin's to Bob's = 4 : 10 : 3
Very difficult question & to solve as well. Is it possible to explain using picture or diagram? Thank you.
I don't have access to writing materials so I'll just use symbols.
Edit : answer with symbols has been posted.
Edit : answer with symbols has been posted.
Since they meet every 4 min,
21min ÷ 4min = 5 R 1min
They would have met for 5 times in total
4(1st time) + 4(2nd time) + 4(3rd time) + 4 (4th time) + 4(5th time) + 1min(not met yet) = 21
Since question asks for how many times did they meet again, this means after the first time, they met again for 4 times.
21min ÷ 4min = 5 R 1min
They would have met for 5 times in total
4(1st time) + 4(2nd time) + 4(3rd time) + 4 (4th time) + 4(5th time) + 1min(not met yet) = 21
Since question asks for how many times did they meet again, this means after the first time, they met again for 4 times.
Since Tom runs 1 round in 7 min, let distance of 1 round = 7 units
Tom runs ⬜⬜⬜⬜⬜⬜⬜ in 7 min
In 2 min, distance Tom ran = ⬜⬜
Remaining distance of the round to run = ⬜⬜⬜⬜⬜
But Kelvin, who started at the same point and time but in the opposite direction,met him there after 2 min.
So in that 2 min, Kelvin must have run ⬜⬜⬜⬜⬜, which is the same distance Tom will have to run to complete 1 round.
In 4 min, distance Tom ran = ⬜⬜⬜⬜
Remaining distance of the round to run = ⬜⬜⬜
But Bob who started at the same point and time but in the opposite direction,met him there after 4 min.
So in that 4 min, Bob must have run ⬜⬜⬜, which is the same distance Tom will have to run to complete 1 round.
So,
Tom ran ⬜⬜⬜⬜ in 4 min.
Bob ran ⬜⬜⬜ in 4 min.
Kelvin ran ⬜⬜⬜⬜⬜ in 2 min.
So in 4 min (which is twice of 2 min), Kelvin ran twice of that , which = ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
Ratio of Tom speed : Bob : Kelvin =
⬜⬜⬜⬜ : ⬜⬜⬜ : ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
= 4 : 3 : 10
(Note : to find speed in terms of per minute, we would divide each distance by 4
Tom = 4 units ÷ 4 min = 1 unit/min = 4/4 units/min
Bob = 3 units ÷ 4 min = ¾ units/min
Kelvin = 10 units ÷ 4 min = 10/4 units/min
Realise that the ratio 4/4 : 3/4 : 10/4 still simplifies to 4 : 3 : 10.
So we don't actually have to find out the speed per min to get the ratio, since we are dividing all by the same number of minutes. Just need to compare their distances run in the same time. )
Tom runs ⬜⬜⬜⬜⬜⬜⬜ in 7 min
In 2 min, distance Tom ran = ⬜⬜
Remaining distance of the round to run = ⬜⬜⬜⬜⬜
But Kelvin, who started at the same point and time but in the opposite direction,met him there after 2 min.
So in that 2 min, Kelvin must have run ⬜⬜⬜⬜⬜, which is the same distance Tom will have to run to complete 1 round.
In 4 min, distance Tom ran = ⬜⬜⬜⬜
Remaining distance of the round to run = ⬜⬜⬜
But Bob who started at the same point and time but in the opposite direction,met him there after 4 min.
So in that 4 min, Bob must have run ⬜⬜⬜, which is the same distance Tom will have to run to complete 1 round.
So,
Tom ran ⬜⬜⬜⬜ in 4 min.
Bob ran ⬜⬜⬜ in 4 min.
Kelvin ran ⬜⬜⬜⬜⬜ in 2 min.
So in 4 min (which is twice of 2 min), Kelvin ran twice of that , which = ⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜
Ratio of Tom speed : Bob : Kelvin =
⬜⬜⬜⬜ : ⬜⬜⬜ : ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
= 4 : 3 : 10
(Note : to find speed in terms of per minute, we would divide each distance by 4
Tom = 4 units ÷ 4 min = 1 unit/min = 4/4 units/min
Bob = 3 units ÷ 4 min = ¾ units/min
Kelvin = 10 units ÷ 4 min = 10/4 units/min
Realise that the ratio 4/4 : 3/4 : 10/4 still simplifies to 4 : 3 : 10.
So we don't actually have to find out the speed per min to get the ratio, since we are dividing all by the same number of minutes. Just need to compare their distances run in the same time. )
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