# math

posted by .

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

• math -

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 ---- ✔

• math -

this is a little bit hard,still not understand

## Similar Questions

1. ### English

1. He has as many books as Tom. 2. He has as much money as Tom. 3. He is as strong as Tom. 4. He runs as fast as Tom. 5. He jumped rope more than Jane. 6. Tom jumped rope as many as Mike. (Are they all grammatical?
2. ### math

Let AB be a diameter of a circular track. Tom starts from point A running clockwise on the track. At the same time Jerry starts from Point B running counterclockwise on the track. Each person runs at a constant speed. They first meet …
3. ### math

In a motorcycle race, one lap of the course is 650 m. At the start of the race, John sets off 4 seconds after Tom does, but John drives his motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than Tom does. What is the speed …
4. ### math

In a motorcycle race, one lap of the course is 650 m. At the start of the race, John sets off 4 seconds after Tom does, but John drives his motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than Tom does. What is the speed …
5. ### maths

A) Sam jogs 6 laps around a circular running track which has a radius of 30 meters. How far does she jog in total?
6. ### Maths

A)Sam jogs 6 laps around a circular running track which has a radius of 30 meters. How far does she jog in total?
7. ### Math

Tom can complete 5 laps of a race track in 15 minutes. Mark can finish 10 laps in 20 minutes at a speed of 150 miles/hour. How fast is Mark driving compared to Tom?
8. ### maths

sarah, tom and johns were all friiends. sarah and john were surprised to know that tom didn't know how old they were. sarah: if you add athird of my age to three quartes of toms age you get, 30.5 tom: if you take my age and double …
9. ### English

1. He is less tall than Tom. 2. Tom is taller than he. 3. He is less smart than Tom. 4. Tom is smarter than he. 5. He is less big than Tom. 6. Tom is bigger than he. 7. He is less careful than Tom. 8. Tom is more careful than he. 9. …
10. ### English

1. Tom is one year older than John, 2. Tom is twice older than John. 3. Tom is twice as old as John. 4. Tom is a little older than John. 5. Tom is two years older than John. 6. Tom is older than John by two years. 7. Tom is much older …

More Similar Questions