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In a 1000 m race, A gives B a start of 40 m and beats him by [#permalink]
17 Aug 2004, 18:02

In a 1000 m race, A gives B a start of 40 m and beats him by 19 seconds. If A gives B a start of 30 seconds, B beats A by 40 m. Find the ratio of their respective speeds.

Not sure if I'm right working out this way, my gut feeling is I'm wrong as the ratio has a crazy number. But here it is.. if its' wrong, will be glad to see the solution !

Let A and B be the speed of A and B respectively. Then

1000/A - 960/B = 19 secs (From statement 1)

1040/B - 1000/A = 30 secs (From statement 2)

So solving gives B = 80/49 meters per second
and A = 1000/607 meters per second

So the ratio A/B = 1225:1214

I think I'm definitely wrong, but that's how I interprete the statements.

Not sure if I'm right working out this way, my gut feeling is I'm wrong as the ratio has a crazy number. But here it is.. if its' wrong, will be glad to see the solution !

Let A and B be the speed of A and B respectively. Then

1000/A - 960/B = 19 secs (From statement 1)

1040/B - 1000/A = 30 secs (From statement 2)

So solving gives B = 80/49 meters per second and A = 1000/607 meters per second

So the ratio A/B = 1225:1214

I think I'm definitely wrong, but that's how I interprete the statements.

From 1st fact, when A travels 1000 m, B manages to travel only 1000-40=960m. Also, B gets beaten by 19 seconds. Hence, B travels MORE by 19 seconds compared to A's time.

So you get, (1000/v1) = (960/v2) - 19 (you have to take out 19, rather than add 19 to balance the equation, as B's time is more).

From the second fact, you get, (960/v1) = (1000/v2) - 30 (Here again we take out 30 seconds, as B travels MORE by 30 seconds).

You really cannot use 1040 in the second equation, as it will mess up your time ratio. A does not travel more than the length of the race.

But if B is beaten by 19 seconds, that means when A reaches the finishing line, B is still 19 seconds behind. So 19 seconds should be added if we want to equate both sides, shouldn't we?

But if B is beaten by 19 seconds, that means when A reaches the finishing line, B is still 19 seconds behind. So 19 seconds should be added if we want to equate both sides, shouldn't we?

The way I understand it is, if X beats Y by 19 seconds, that means that X is faster and Y is slower. Hence X reaches finishing line in less than (19 seconds) than Y. That means that Y will still travel 19 MORE seconds after X has already reached the finishing line. So if you are comparing time, you need to take out 19 seconds from the slower guy to equal them up.

If you look at the statement "In a 1000 m race, A gives B a start of 40 m and beats him by 19 seconds". That means that A has beaten B in the race. That means that both A and B NEED TO COMPLETE the race if one of them has to be beaten.

If I am not wrong, your interpretation of the statement is, at the time when A reaches finishing line, B is "19 seconds behind A" and race is over. But if you interpret it like that, that means that B still has not completed the race. If B has not completed the race yet, he cannot be beaten. He can only be beaten when he actually completes the race (atleast in our situation )

That's exactly how i interpreted the question ! I suppose we can't assume too much when we deal with these questions ! This one will go into my notebook

I really thought about this, and this is the conclusion I came to. If A beats B in time, than we need to take time out of B to equal their TIMES. Alternatively, if A beats B is distance, than we need to add distance to B to equal their DISTANCES.

That's a really interesting way to look at it. I got a little confused when the question started going into how much time B is beaten. I just kept thinking whether to add or not. I guess this method is a great way to remember !