Question

Sam was still finishing his breakfast when his brother Leo left for school. Sam started to run after Leo when Leo was already 100 meters away. How soon will Sam catch up, if he is running at a speed of 105 meters per minute while Leo is walking at a speed of 65 meters per minute?

Answer 1

Sam will catch up his brother in 2.5 minutes

Explanation:

Two equations can be written to represent the problem.

Sam: y1 = 105*t

Leo: y2 = 100 + 65*t

where y represent position, in meters, and t is time in minutes. That is, after 1 minute after Sam started to run, Sam will be at 105 meters of distance from the house, and Leo will be at 165 meters of distance from the house.

When Sam catch up Leo, the distance travelled by both equals:

y1 = y2

105*t = 100 + 65*t

105*t - 65*t = 100

40*t = 100

t = 100/40

t = 2.5 minutes