Math Help - Maths help.

1. Maths help.

Sorry I don't know where I should post this thread so I'll it here. Apologies if its in the wrong section.

Help on this maths problem:

In a 100 metres swimming competition John beat Jim by 10 metres, and Jim beat Ken by 20 metres. By how much did John beat Ken, if all swimmers had a constant speed?

2. Originally Posted by xxravenxx
Sorry I don't know where I should post this thread so I'll it here. Apologies if its in the wrong section.

Help on this maths problem:

In a 100 metres swimming competition John beat Jim by 10 metres, and Jim beat Ken by 20 metres. By how much did John beat Ken, if all swimmers had a constant speed?

That would have been my guess! The difference, of course, is that Ken was 20 m behind Jim when Jim finished the race, not when John finished the race. Since Ken finished behind Jim, he was swimming slower and so would have lost ground in the time between John and Jim finishing. When John finished, Ken must have been closer than 20 m behind Jim.

Let's see. Suppose John swims at speed v metres per second. Then he would have finished in 100/v seconds.

Since Jim was then 10 metres behind, he swam 90 meters in 100/v seconds and so was swimming at the rate of (90)(v/100)= (9/10)v. At that rate he will have completed the race in 100((10/9)v)= 1000/(9v) seconds.

Since Ken was 20 metres behind Jim, he swam 80 meters in 1000/9v seconds so he was swimming at the rate of (80)(9v/1000)= (72/100)v.

When John finished the race, in 100/v seconds, Ken had also been swimming for 100/v seconds and so had gone (100/v)(72/100)v= 72 metres. Ken was 100-72= 28 meters behind John!

3. Hello, xxravenxx!

This is a classic trick question.

My solution is the same as HallsofIvy's . . . different language.

In a 100-m swimming competition John beat Jim by 10 m, and Jim beat Ken by 20 m.
By how much did John beat Ken, if all swimmers had a constant speed?

"John beat Jim by 10 m."
When John swam 100 m, Jim swam only 90 m.

"Jim beat Ken by 20 m."
When John swam 100 m, Ken swam only 80 m.
Proportionately, when John swam 90 m. Ken swam 72 m.

Hence, in the race: . $\begin{Bmatrix}\text{John swam 100 m,} \\ \text{Jim swam 90 m,} \\ \text{Ken swam 72 m.} \end{Bmatrix}$

Therefore, John beat Ken by: $100 - 72 \:=\: 28\text{ m.}$