A and B were running alone the 400m track. They started on the same point and at the same time. A's speed was 6meter/second and B progress at a speed of 4meter/second. When A exceed B by one lap, how many laps would B have run?
2006-07-05 09:34:32 · 14 answers · asked by MichelleC 2 in Science & Mathematics ➔ Mathematics
The Equation is 6t=4t+400. 6t is A's distance, and 4t+400 should equal A's speed because it is B's distance, plus an xtra lap, because you want A to exceed B by one lap. When you solve for t, you are solving the number of seconds it takes for both of them to equal each other.
6t=4t+400
6t-4t=4t-4t+400
2t=400
t=200.
It would take 200 seconds for A to exceed B by one lap.
Plug it back in:
A: 6 meters/second with 200 seconds is 1200 meters
B: 4 meters/second with 200 seconds is 800 meters
There is a one Lap difference between the two, since 1200-800=400 and 400 meters is one lap.
B has ran 800 meters.
800 meters is 2 laps [800/2=400]
2006-07-05 10:01:18 · answer #1 · answered by Anonymous · 2⤊ 1⤋
All you have to do is set up the ratio: the speed of a (6m) is to the speed of b (4m) as a's number of laps (number of laps of b plus one) is to b's number of laps. So if we call b's number of laps x, then:
6/4 = x+1/x
which we can work out to 6x = 4x+4
and which solves to x=2
So B will have run two laps and A will have run 3.
2006-07-05 09:50:07 · answer #2 · answered by Clockwork 1 · 0⤊ 0⤋
Good!
A lap is usually what? 400m? Who cares?
Did you say "When A exceed B by one lap," so B would have to run 1 more lap. This is not a mathematical problem but a play on word or a pun.
2006-07-05 09:37:02 · answer #3 · answered by Edward 7 · 0⤊ 0⤋
(rate) (time) = distance
You're given the rates for both A and B, and the other information you have regards distance. You don't know how much time, so choose a variable to represent it. (I'm picking "t" for time in seconds.)
(6 meters / second) (t seconds) = 6t meters, the distance A runs.
(4 meters / second) (t seconds) = 4t meters, the distance B runs.
A ends up, after t seconds, one lap (400 meters) ahead of B.
A's distance = B's distance + 400 meters.
6t = 4t + 400
Solving for t is simple enough...
6t - 4t = 4t + 400 - 4t
2t = 400
t = 200.
The solution to your equation isn't the answer to your problem, though, is it? It tells you how many seconds the race took, but you're supposed to find out how many laps B ran.
You know B's distance in meters is 4t. You know t is 200. You know 400 meters is one lap.
Laps = 4t / 400. You know the rest. :-)
2006-07-05 10:35:42 · answer #4 · answered by Anonymous · 0⤊ 0⤋
there are two parts to this problem:
1. How long will it take for A to get 400m ahead of B
2. In that amount of time, how far will B have run?
1. 6 m/sec - 4 m/sec = 2 m/sec difference
..... (400m)/(2m/sec) = 200 seconds
2. 200sec*4m/sec = 800m = 2 laps
2006-07-05 10:10:22 · answer #5 · answered by ♥Tom♥ 6 · 0⤊ 0⤋
it really is not exhibits about undesirable wellbeing in any respect! you in ordinary words were given somewhat rusty in calculating this. So, the first calculation is incorrect, because a million-(a million-5) isn't equivalent to at least a million-a million-5. you won't be able to upload the brackets to it. imagine about it that way- in a million-a million-5, we take the volume a million. Then, we eliminate a million from it, and then, we eliminate 5 from the outcome. So, because that we eliminate both a million and 5, we are able to assert, that we in ordinary words ought to calculate a million-(a million+5). You eliminate both a million and 5 together. So, it really is a million-6: -5. that is that undemanding.
2016-11-01 06:24:29 · answer #6 · answered by ? 4 · 0⤊ 0⤋
'A' is lapping the track in 66.6secs which is 33.3secs faster than 'B' who laps it in 100secs. So when 'A' has lapped it 4 times 'B' will have lapped it 3 times. So the answer is 'B' will have completed 3 laps.
2006-07-05 09:43:46 · answer #7 · answered by Woodentop 3 · 0⤊ 0⤋
6t = 4t + 400
6t is the number of meters A would have run in t number of seconds
4t is the number of meters B would have run in t number of seconds
400(m) is the difference between the two runners at a certain time t.
When you solve for t, 4t is what B would have run.
4t/400 is the number of labs B would have run.
The remainder is left for the student.
2006-07-05 09:37:59 · answer #8 · answered by revicamc 4 · 0⤊ 0⤋
there is no equation because both speeds are constant, therefore b would never be able to catch up to a so long as a continues to run. perhaps you need to re-word this question so that a sufficient answer can be given.
2006-07-05 09:39:12 · answer #9 · answered by mmenaquale 2 · 0⤊ 0⤋
divide 400 by 6meters/second same hold on I'm not your math tutor
2006-07-05 09:39:44 · answer #10 · answered by gil3moj@yahoo.com 2 · 0⤊ 0⤋