racing puzzle

[FAIZE]

Three people from ABC will compete in a one-on-one 100m race.

Everyone runs at a constant speed.

A beats B by 20 yards.(métres)
B beats C by 20 yards.(métres)

Now, if A and C face each other, how many meters will A beat C?

 

[topsquark]

Three people from ABC will compete in a one-on-one 100m race.

Everyone runs at a constant speed.

A beats B by 20 yards.(métres)
B beats C by 20 yards.(métres)

Now, if A and C face each other, how many meters will A beat C?

Motion in 1D with constant velocity can be modeled by the equation
[imath]x = vt[/imath]

So let A's speed be denoted by [imath]v_A[/imath], etc. Call the time the races run [imath]t_1[/imath] and [imath]t_2[/imath].

Then for race 1:
[imath]100 = v_A t_1[/imath]

and we know that B is lagging behind A by 20 m, so
[imath]100 - 20 = v_B t_1[/imath]

For race 2:
$[imath]100 = v_B t_2[/imath]

and we know that C is lagging behind B by 20 m, so
[imath]100 - 20 = v_C t_2[/imath]

Hint:
Race 3 would be between A and C. So
[imath]100 = v_A t_3[/imath]

and
[imath]100 - d = v_C t_3[/imath].

Can you finish?

-Dan

 

[FAIZE]

Motion in 1D with constant velocity can be modeled by the equation
[imath]x = vt[/imath]

So let A's speed be denoted by [imath]v_A[/imath], etc. Call the time the races run [imath]t_1[/imath] and [imath]t_2[/imath].

Then for race 1:
[imath]100 = v_A t_1[/imath]

and we know that B is lagging behind A by 20 m, so
[imath]100 - 20 = v_B t_1[/imath]

For race 2:
$[imath]100 = v_B t_2[/imath]

and we know that C is lagging behind B by 20 m, so
[imath]100 - 20 = v_C t_2[/imath]

Hint:
Race 3 would be between A and C. So
[imath]100 = v_A t_3[/imath]

and
[imath]100 - d = v_C t_3[/imath].

Can you finish?

-Dan

if B runs 80 m, C runs how long ?

 

[Dr.Peterson]

if B runs 80 m, C runs how long ?

That's how I'd approach it.

Are you proposing this as a puzzle for others to try, and giving a hint because you actually know the answer? If so, you need to explicitly tell us that, so we don't think we're supposed to help you solve it.

If I were giving a hint, I might say,

When A runs 100 m, B runs 80 m.​

When B runs 100 m, C runs 80 m.​

How far does C run while A runs 100?​

 

[topsquark]

if B runs 80 m, C runs how long ?

I leave that to you... It's only a small change from the format I suggested for you.

Post what you get and we'll take a look at it.

-Dan

 

[FAIZE]

If A runs 100m, B runs 80m.
If B runs 100m, C runs 80m; so if B runs 80m, C runs 64m.

If A and C play each other, A will win by 36m.

 

[khansaheb]

If A runs 100m, B runs 80m.
If B runs 100m, C runs 80m; so if B runs 80m, C runs 64m.

If A and C play each other, A will win by 36m.

Correct.

 

[topsquark]

If A runs 100m, B runs 80m.
If B runs 100m, C runs 80m; so if B runs 80m, C runs 64m.

If A and C play each other, A will win by 36m.

IF A and C play against each other and run 100 m, THEN A will win by 36 m.

Please post your full solution.

-Dan