Question

person a wants to walk to person b's house that is 3 miles away. person a's walking speed is 3 mph while person b's biking speed is 12m, 4 minutes later person a's mom notices person a forgot something and sends person a's brother to get it, how fast should person a's brother travel to catch up to person a?

Answer 1

Answer: 2.8 mph

Explanation:

First find distance traveled in 4 min by person a.

D=s*t, you get 0.2 miles. So in 4 min, person a traveled 0.2miles.

Distance=3*1/15= 1/5 which equals 0.2 miles.

(t should be in hours since mph, so 4/60, which is simplified tp 1/15)

2. Use concept of relative speed

Remaining distance to person B's house is 3-1/5=14/5 or 2.8 miles. Person A's brother has to cover 2.8 miles faster than person A to catch up.

3. let x = speed in mph the brother must travel to catch up to person A. They are moving in the same direction so relative speed is (x-3) mph, or brothers speed minus person A's speed.

4. Time needed for the brother to catch up to person A = time it takes for Person A to reach person B's house

To find time we can use: Time= Distance/Speed

Person A's brother: Time=14/5 over x

Person A: Time= 3/3=1 hour

Setting these equal to each other gets 14/5 over x=1

5. Solve for x.

Multiply by x to get 14/5.

x= speed the brother needs to travel to catch up, which is 14/5 or 2.8 mph.