Another Racing Problem

Bob, John and Josh are running a 1 km race. Each competitor runs at a constant rate.

After Bob has run 1/4 km, Bob is ahead of John by 25 meters.
After John has run 1/2 km, John is ahead of Josh by 20 meters.

When Bob finishes the race, by how much distance does he beat Josh?

@joe-shmo said
Bob, John and Josh are running a 1 km race. Each competitor runs at a constant rate.

After Bob has run 1/4 km, Bob is ahead of John by 25 meters.
After John has run 1/2 km, John is ahead of Josh by 20 meters.

When Bob finishes the race, by how much distance does he beat Josh?

@venda said
Bob beats John by 100 mtrs
John beats Josh by 40mtrs.
So Bob beats Josh by 140 mtrs

@joe-shmo said
Sorry, Try again.

@venda said
Half way thro' the race:-
Bob = 500mtrs
John = 475mtrs
Josh = 455 mtrs
500*2 = 1000
475*2 =950
455*2 = 910
Therfore Bob beats Josh by 90mtrs

@joe-shmo said
unfortunately...your getting further away.

@venda said
I wrote it down this time.
Is it 40?

@joe-shmo said
Nope

@venda said
Oh well.
I used to do these things all the time.
I'm obviously a little out of practice(and a lot older)
I'll let someone else have a go.
Thanks anyway

@joe-shmo said
Thanks for trying! If you want to give it another go later on, feel free to do so. If you don't figure it out, you'll kick yourself when you see it.

@venda said
Don't do kicking anymore.
Got an arthritic hip!!
From your tone I think there might be a catch in the wording.
However once more:-
After 250 mtrs run by Bob, John has run 225 mtrs Josh has run 215 mtrs
This means Bob is 45 mtrs in front of Josh
4*250 =1Km
4*45 = 180 mtrs behind.
180mtrs -final answer!! and I've used all my lifelines!!

@joe-shmo

136m?

@blood-on-the-tracks said
@joe-shmo

136m?

Solution:

For every 250 meters Bob goes, John Goes 225 meters.

When Bob has traveled 1000 meters ( The end of the race for Bob ), John has travled 225*4 = 900 meters

For every 500 meters John travels, Josh travels 480 meters.

At the time Bob crosses the finish line Josh has traveled:

480*( 900 / 500 ) = 864 meters

Thus, the distance between Bob and Josh at the finish is:

1000 meters - 864 meters = 136 meters

Problem taken from:

https://brilliant.org/problems/winning-is-not-the-strategy/

More racing Problems:

A, B, and C are running a race. The probability of A winning is twice that of B winning. The probability that B winning is twice that of C winning. The probability of any ties is zero. What is the probability "A" wins the race?