Person a leaves his home to visit his cousin, person b, who lives 263 miles away. he travels at an average rate 46 miles per hour. one half-hour later, person b leaves her house to visit person a, traveling at an average rate of 74 miles per hour. how long after person bleaves will it be before they meet?

It will take 2 hours after person B leaves before they meet

Step-by-step explanation:

Step 1: Determine expression for calculating speed, distance and time

The expression for calculating distance, speed and time is;

d=s×t

where;

d=distance in miles

s=speed in miles per hour

t=time in hours

Step 2: Distance covered by person A after 0.5 hours

In this case;

d=unknown

s=46 miles per hour

t=0.5 hours

replacing;

d=(46×0.5)=23 miles

Step 3: Determine the remaining distance to person B house

Remainder=Total distance-distance already covered by person A

where;

total distance=263 miles

distance already covered by person A=23 miles

replacing;

Remainder=(263-23)=240 miles

Remaining distance to person B house=240 miles

Step 4: The time it will take for them to meet

The only have a distance (d) of 240 miles left to cover

Since they are moving towards the same direction, there speeds (s) are added together=(46+74)=120 miles per hour

replacing in the expression below;

time=distance/speed

time=(240/120)=2 hours

It will take 2 hours after person B leaves before they meet