john and tom race around a circular track,divided like the face of a clock,into 12 sections.if john gives tom 4 sections start in advance and runs half as fast as tom.at what point on the track will he overtake tom
When they meet,
let the number of laps covered by John (the slower) be n
So number of sections covered by John = 12n
In that same time, Tom has covered 12n-4 sections
Time = distance/rate
Tom's time = 12n/2
John's time = (12n-4)/1
12n/2 = 12n-4
6n = 12n-4
6n=4
n= 2/3
He will catch him at the 8 section mark of the first lap
Tom's time = 12n/2 = 6n = 6(2/3) = 4 units of time
John's time = (12n-4)/1 = 12(2/3)-4 = 4 units of time ----- ✔
Tom's rate = Tom's distance/4 = 8/4 = 2 units of distance/units of time
John's rate = 4/4 = 1 unit of distance/time ---- ✔
this is a little bit hard,still not understand
To determine at what point on the track John will overtake Tom, we can break down the problem into smaller steps and use some simple calculations.
Step 1: Calculate the number of sections Tom can complete in the time it takes John to catch up.
Since John runs half as fast as Tom, it means Tom will cover twice the distance that John covers in the same amount of time.
Therefore, if Tom runs x sections, John will run x/2 sections.
Step 2: Calculate the number of sections John needs to catch up.
Since John gives Tom a 4-section head start, John needs to catch up by running 4 sections more than Tom.
So, the number of sections John needs to run to catch up is x/2 + 4.
Step 3: Determine the position on the track where John will overtake Tom.
Since the track is divided into 12 sections like a clock, we need to determine the point on the track corresponding to the number of sections John needs to run to catch up.
To do this, we can assume that one complete lap around the track is equivalent to 12 sections. Therefore, we need to find the remainder when (x/2 + 4) is divided by 12.
Using the remainder, we can determine the point on the track where John will overtake Tom.
Let's illustrate this with an example:
Suppose Tom runs 8 sections, which means John needs to run (8/2) + 4 = 8 sections to catch up.
To find the point on the track, we can calculate the remainder of 8 divided by 12.
8 divided by 12 gives a quotient of 0 and a remainder of 8.
Therefore, John will overtake Tom at the 8th section around the circular track.
You can apply the same steps and calculations with different values for Tom's sections to find out when and where John overtakes him.