You and Tom are having a biking race. You can bike 400

meters per minute, and your brother can bike 420 meters

per minute. You start 200 meters in front of the starting

line while Tom starts on the starting line. After how many

minutes will you and Tom be same distance from the

starting line?

Answer: After 10 minutes

Step-by-step explanation:

Let Distance to be traveled be=D,

But you have a head start of 200 meters, therefor the distance you need to cover is reduced the expression becomes=D-200

Tom starts from the starting line so his distance=D

Since we need the time when Tom and you will meet, we equate the time Tom takes with his speed to the time you take with your speed to cover respective distances

Since Time=Distance/speed

Tom's time can be expressed as=D/420 equation 1

Your time can be expressed as = (D-200) / 400 equation 2

Equating equation 1 and 2

(D/420) = (D-200) / 400, solving

420 (D-200) = (400) D

420D-84000=400D

420D-400D=84000

20D=84000

D = (84000/20)

D=42000

To get the time that they will meet, we substitute the value of D on either equation 1 or 2

(4200-200) / 400=10 minutes