Question

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?

Answer 1

Person A has traveled 23 miles in the first half-hour, leaving 240 miles to meet. Their combined speed is 120 mph, so it will take 2 hours after person B leaves for them to meet.

Step-by-step explanation:

To determine how long after person B leaves will it be before they meet, we need to set up an equation that accounts for both person A and person B's travel distance and speed. Person A starts half an hour earlier, so they will have already traveled a certain distance before person B starts his journey.

We start by calculating the distance person A has traveled in that first half-hour, which is at a rate of 46 miles per hour. We use the formula Distance = Speed × Time to get:

Distance A has traveled in the first half-hour = 46 mph × 0.5 hours = 23 miles.

This means that when person B starts, the remaining distance they need to meet is:

Remaining distance = Total distance - Distance A has traveled = 263 miles - 23 miles = 240 miles.

Since they are now both traveling towards each other, their speeds add up. Therefore, their combined speed is:

Combined speed = Person A's speed + Person B's speed = 46 mph + 74 mph = 120 mph.

Now, we can find out how long it will take them to meet by using the remaining distance and their combined speed:

Time to meet = Remaining distance ÷ Combined speed = 240 miles ÷ 120 mph = 2 hours.

Thus, it will take 2 hours after person B leaves for them to meet.

Answer 2

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