# Math Help - father and son problem

1. ## father and son problem

I need help in the below question.

There are a father and a son. While the father covers 4 steps, the son covers 3 steps. The father covers a distance by 4 steps and the son covers the same distance by 5 steps. If the son covers 60 m, how many metres will the father cover?

2. ## Re: father and son problem

Originally Posted by kingman
I need help in the below question.

There are a father and a son. While the father covers 4 steps, the son covers 3 steps. The father covers a distance by 4 steps and the son covers the same distance by 5 steps. If the son covers 60 m, how many metres will the father cover?
conflicting information? should the 3 steps be 5 steps in the first sentence ... typo, maybe?

3. ## Re: father and son problem

Originally Posted by skeeter
conflicting information? should the 3 steps be 5 steps in the first sentence ... typo, maybe?

no typo error and answer is 100m

4. ## Re: father and son problem

Originally Posted by kingman
I need help in the below question.

There are a father and a son. While the father covers 4 steps, the son covers 3 steps. The father covers a distance by 4 steps and the son covers the same distance by 5 steps. If the son covers 60 m, how many metres will the father cover?
Let's say the son does $\frac{60}{4} = 15$ metres/step.

Since the father covers 4 steps for every 3 steps the son does, he will cover $15 \times \frac{4}{3} = 20$ metres/step.

Then the distance the father covered is $\frac{d}{5} = 20 \Rightarrow d = 100$ metres.

5. ## Re: father and son problem

15 meters per step? That's a heck of a long legged kid! Skeeter, the information given is not conflicting. The first sentence tells us how many steps they take in a fixed time, the second the relative distance per step.

6. ## Re: father and son problem

Question is poorly worded, then ... imho.

7. ## Re: father and son problem

the father's speed is 4/3 of the son's speed, regardless of the units.

the father's stride is 5/4 the size of the son's stride, again, regardless of the units.

so if the son covers 60 meters, in the same amount of time the father will cover (4/3)(5/4)(60) = 100 meters.

8. ## Re: father and son problem

Can you please explain why the first statement in question suddenly becomes speed comparison between father and son as
claimed by your solution when both father and son step-length are different as implied in the questionn
'the father's speed is 4/3 of the son's speed, regardless of the units'.

So in the question the known variables are frequency of father and son steps are in the ratio 4:3 and similarly ratio of father and son speed is 1/4 father step-length: 1/ son step-lenght which I cannot see how this will led to the corressponding ratio 4:5.

Thanks

9. ## Re: father and son problem

"While the father covers 4 steps, the son covers 3 steps"

the ratio of father steps to son steps is 4:3. the units are steps/steps, that is, dimensionless (this is often the case with ratios).

so how many steps does the father take when the son takes one? (1/3)(4) = 4/3 (1 is one third of 3, so 4/3 is one third of 4).

"The father covers a distance by 4 steps and the son covers the same distance by 5 steps"

each step of the father is D/4, each step of the son is D/5 (D being "a distance"). thse are in the ratio D/4: D/5 = 5:4

((D/4)/(D/5) = (D/4)(5/D) = 5D/(4D) = 5/4). so the father covers 5/4 the distance the son does with each step.

we don't know how many steps the son took, or how long it took him to cover the distance, but we do know he covered 60 meters.

in that same amount of time, the father took 4/3 the amount of steps, and covered 5/4 the distance the son did with every step.

10. ## Re: father and son problem

Originally Posted by HallsofIvy
15 meters per step? That's a heck of a long legged kid! Skeeter, the information given is not conflicting. The first sentence tells us how many steps they take in a fixed time, the second the relative distance per step.
I know, my method was bothersome to me, but the question simply stated "distance" and I went with the full 60m. It's arbitrary anyway.

11. ## Re: father and son problem

Originally Posted by janvdl
I know, my method was bothersome to me, but the question simply stated "distance" and I went with the full 60m. It's arbitrary anyway.
indeed it's just a problem concerning ratios, or proportions. the only units that actually enter into it, are the meters that we take the proportion of, at the end.

12. ## Re: father and son problem

(4/3)(5/4)(60) = 100 meters.

Trying to figure out why you are multiplying those together.

60m is what the son traveled.

5/4 is the steps the son and dad take to go the same distance.

4/3 is the speed they walk at.

I know it works, I just am having trouble figuring out why. 5:4 • 60 gets you what? that times 4/3 gets you what?

13. ## Re: father and son problem

Code:
Dad  | 5 | 5 | 5 | 5 | : 20 * 5 = 100
Son  | 4| 4| 4[ 0| 0 ] : 12 * 5 =  60